Q: how to downgrade from el capitan no time machine back up

Instead of downloading which is going to be either extremely difficult if not impossible without a backup, I suggest you download and install EtreCheck from http://etrecheck.com/ Run it and post the report here.

The only way to preserve your data is to make a good backup before you begin. Always keep your Mac backed up on an external disk with either Time Machine and/or a cloning utility like SuperDuper or CarbonCopy Cloner.

In order to downgrade, you need to do a erase and install:

Boot holding the command + option + r keys and follow the steps for Internet Recovery in this Apple Support Article:

https://support.apple.com/en-us/HT204904

Erase and install deletes EVERYTHING. All your files, Tunes movies.

Do not even THINK about doing that until you have made a backup.

Buy your self an external drive, BIG (3 times the size of your stuff or more) but it does not have to be FAST. Turn on Time Machine, and the first big backup will be done in an afternoon. The next one is an incremental backup, and will be really fast, but it will not interfere with what you are doing at all.

Once you turn on Time Machine, it will take care of doing the incremental backups after the first full backup.

It just does it, roughly hourly. You keep working and don't lift a finger. Time machine works in the background and does not slow down the work YOU want to keep doing.

The first thing to do is to create a Time Machine backup: Use Time Machine to back up or restore your Mac - Apple Support.

Then, you can explore some options, including determining just what is causing your Mac to become slow.