I think a lot depends on the exact period we're talking about.
I'd toss out the Albigensian crusade (1210+) as a sort of turning point - it was that gesture from the Pope that threw open the gates for "worldly interests" from the viewpoint of The Church. Before then, it was all about God - after, it was about being strong on a temporal level as well. The typical 1200 Ars game is in between these, when the church is seen as becoming decadent, but not there yet.
Long before that, monestaries were walled communities, largely self sufficient, and so had neither unknown strangers wandering about nor much traffic in general, so your average bandit group would not know where to look if they were trying stealth, and would have to be fairly numerous (and ballsy) to try strength. "Armed security" probably did not exist as such (images of armoured guards leaning on their spears outside a door - not so much), but many monks were ex-military, or at least knew how to handle themselves, depending on the Order - it would have taken a serious force to breech the walls and then take the entire monestary long enough to search/find/ransack any strongroom (or the sort of "plan" you usually only see in Hollywood... or RPG's, admittedly.)
While a monastary was a community and thus largely separate from the hierarchy of the mother Church, anything less than a Cathedral probably could not say the same. So, while monks could do as they pleased, a priest or even bishop might have immediate superiors to answer to. (And the "walls" thing was a big part of the security - that and the isolation. Churches ~did~ have constant traffic, far more frequent strangers about, and fewer secrets in general because of that. Also, being usually immediately adjacent to an urban center of some sort, the temptation would have been greater and the "plan" less necessarily complex.)
"Warrior monks" (like the Templars?) were an exception rather than a rule, and were often both less holy (or perceived that way?) and located in more belligerent areas.
Reliquaries would probably not have any security other than a locked door, and perhaps not even that, depending. Some chapels had stuff "sitting around", and were somewhere between naive and simply in denial of the target they had on themselves.
Those Monasteries and Churchmen who where land owners would employ soldiers in the same manner as mundane land lords to enforce law and order , they would not be garrisoned at the monastery. At least one bishop was seized by King Richards men leading knights in the service of the French King against the English in Normandy so there are certainly precedents for them being armed .
It would be quite possible for Monasteries to have a few big and burly lay brothers or even monks around. A lot would depend on how pious the monks.
Monasteries wouldnot normally have large walls as they where not fortified as such (although Monsasteries in turbulent lands may have been) as an example Kirkstall Abbey located down the road from me leeds.gov.uk/kirkstallAbbey/ ... y/Map.aspx
Has no walls or fortifications of any sort and is in a compeltely undefensible location as it is within bowshot of much higher ground on either side of the River.
Knights Templar etc had their own chapter houses and most of them where in the Holy Land although eventualy they would aquire signifignat land grants across Europe and some of their members (Often older or injured Knights) would be involved in administering them. I think it is the Knight templars who provided letters of credit but I am not sure when they started doing so. These would not be associated with the more traditional monasteries.
At least as far back as the 4th Crusade the church played a role in helping crusaders by administering their lands in their abence of converting their assets to something more useful to support a crusader
Uhm, no I can't imagine them doing so. Monestaries may or may not have wealth, but in general this came in the form of donations or bequeths (I hope I am spelling this right). The templar's had a banking network where you could exchange coin in one place for a note, and then redeem the note elsewhere for coin but that was paticular to the Templars.
My mind boggles at the thought a noble would use a monestary or cathedral to store their personal wealth. Also wealth in even this period of time was largely not coin anyway so its hard to see why they would store grain, cows, etc in a monestary rather than on their own lands.
Monestaries generally had at least one building that would count as a "small fortified manor house," some had walls some not. In general they had no security, and warrior monks (unless you mean members of a militant order) didn't exist. But the monks could know how to fight if they would do so is a better question. The local lords troops would likely be called in for security, or there might be a group of pilgrams in the monestary itself.
The fear of god is the primary defence they had. And given the view of the time a lot more effective then you might give it credit for. Also remember that the monestary might be the home to several of the older members of the local nobility so anyone attacking the monestary may make a lot of enemies very quickly.
I'm not 100% sure but I don't think the church was involved in banking. That was handled by families of merchants, as fundamentally there was little need for banking outside of merchants. They needed a way to transport money without moving coin pretty much no else needed to do this. Remember interest is illegal, that is the sin of usary. Churches may have had wealth stored in them (the collections, artifacts, art work etc) and for this the usual trend was there to be a lay "security force" of some sort. But excepting a bishop or higher this was likely more akin to a man that locked the door at night. But if there was substantial amounts of wealth in a church there was likely guards. But again "wealth" was rarely in coins.
The box was locked and was heavy so moving it would be difficult. There were a number of lay individuals up to and including guards with a major cathedral or the church of a bishop. Plus there was the town watch.
Walking away with the alter cups and so forth would be possible but you are risking a lot to do this. Not only physcially but spiritually. Also even a thieves guild might be not inclined to do something of the sort since they are in effect robbing from their own community. Since mass cannot be performed until replacements are produced.
As for the corruption of the church, this didn't start until after the black plauge, according to A Distant Mirror and it seems likely for the reasons given: the loss of a significant number of priests and the gaining of substantial wealth. In the 1200's you can expect that a good chunk of the clergy is infact there to serve their community.
Another point about monestaries is that there were a lot of masses in the day and it would be common enought to find someone just praying or performing penance that moving about the chapter house (assuming the chapel was attached) would be a lot more difficult then it might seem. Also they are a closed community so they would know each other very well.
But if you want to acquire wealth in the form of portable coin or goods a merchant will be a much better target then the local church. I would imagine even at this time a lot of the "donations" to churchs from the local community consisted of goods and services rather than coin.
But I've not done research on this topic particularily so I certainly could be out to lunch on anything I've written.