You can reinstall Firefox over itself. This is useful to repair program files. Generally speaking, you should not lose any personal data/settings when doing this, but it's not a bad idea to do a backup first. This article has tips: Back up and restore information in Firefox profiles.

The steps to do a "clean" reinstall are Step 5 in this article: Troubleshoot and diagnose Firefox problems. Of course, Steps 1-4 are worth a review before doing Step 5.

Regarding your symptoms:

(1) Same links sometimes open in same tab, sometimes in a new window

Does this happen on particular sites? For example, Google has a setting for search results to launch a new window for each result. (If you keep the default Firefox settings, these will be diverted to new tabs.) This is stored in a cookie, so might get deleted occasionally, or be inaccessible in private windows.

More information on the pattern, if any, would be helpful.

(2) All bookmarks in a folder open in tabs

This is the bottom choice when you view a folder of bookmarks, but shouldn't be triggered automatically. Perhaps it is a mouse/trackball incompatibility if simply mousing over it clicks it?

See next post for more on this second symptom

I just noticed I can trigger all bookmarks in a folder to open in tabs if I Ctrl+click or middle-click the folder. Never noticed that before. If you are getting this behavior with a normal left click, there could be a compatibility issue with your mouse/trackball driver/software. Or your Ctrl key is flaky.

Thanks for your help - will try all you have suggested :) Jeff