1990 Honda Accord Engine overheating

I'm not sure what you're referring to. Is that some leakage near the top of the photo, just right of center? If so, that's the thermostat housing. Rather than going through all the trouble of trying to clean it up so glue will stick, just get a replacement from the dealer or from a salvage yard. Without being able to see it closer, it could just be the gasket or seal is leaking. You don't have to replace the entire housing for that.

The common causes are that housing is cracked or the seal is leaking. It's not common for the housing to crack on its own, except on Fords. That normally occurs when one of the bolts is tightened down and there's debris from the old gasket material stuck under it. Some of these housings use a paper gasket that can start to leak. Some use an o-ring set into a groove inside the flat surface of the housing. Those usually leak from corrosion on the housing, not the o-ring seal itself. Both of those conditions occur more often when the coolant isn't replaced every two years. Antifreeze has water pump lubricant and corrosion inhibitors that wear out in about two years. That's why we replace the antifreeze every two years.

A lot of mechanics will reinstall that housing with liquid silicone sealant from a tube instead of a regular gasket. That is perfectly fine except both mating surfaces must be perfectly clean and dry. Most of those sealants will not bond or seal through any oil or water residue.

Depends on whether it's cracked, corroded, or just the gasket is leaking. The thermostat housing needs to be replaced or resealed.

We don't get involved with costs here because there's too many variables, but in this case I would guess a used part, if you pick it up yourself from a salvage yard, might run ten or fifteen bucks, and it should take about a half hour to replace it and address whatever caused the failure.

Be aware that mechanics and shop owners don't like customers providing their own parts. When the shop orders the part, they add on a small markup, just like any other store, but that profit goes to cover their costs if that part proves to be defective. If you provide the part and there's something wrong with it, or it's the wrong part, the job of getting it replaced falls on you. This is similar to bringing your own food to a restaurant and asking them to cook it for you. No one complains when food costs more in a restaurant than in a grocery store, but it's different with car parts.

If you want a new part from the dealer, someone at your repair shop will order it and have it delivered. The part won't cost you any more than if you bought it yourself, but in this case if the mechanic accidentally cracks it, it is up to the shop to pay for the replacement.