Ok, I discovered that part of the problem is that the site is getting to be huge, so I upgraded the package at the webhost (from 4GB Memory & 100GB disk space to 8GB/200GB) - I believe disk space was also causing the problem. phpMyAdmin finally started working again.
But I still cannot figure out what these 'Index...' files are (i.e. 'index_59a95ed158cf8' when viewed in phpMyAdmin) - it would not matter if not for them multiplying like mushrooms (at ~50MB each), which are taking up valuable disk space. Also, on one back-up site I deleted all the tracker files and imported them again fresh (so all item ID's, field names, etc., would match exactly, if using the Tiki Trackers import/export) - before the import, there were like 20 or so, now there are 33! So 1.6GB of the 2.1GB Tiki is just index files - that just doesn't sound correct. This back up is on my personal website and very realistic that I'll hit my 10GB limit and have to move up to a VPS - I just don't need the headaches of managing my own server right now.
Desperate for some advice - Is something incorrect with my Tiki admin or server configs that are causing the index files to constantly duplicate? can I safely delete some of these index files via phpMyAdmin?