how many fish can I fit?

No CAE, they can reach 8-10 inches, and the larger they get the more aggressive and territorial they become.
All tetra, danio and platy should be fine choices, as well as one gourami. In a ten gallon you don't want to overcrowd them.
If you get danio, limit it to maybe 4-5, they are quick, fast moving little zippy fish and you shouldn't crowd them. But they are schooling fish and need a group.
Be careful mixing long finned danio with tetra as tetra are known fin nippers. However, the danio are generally faster than them.
The tetra are schooling fish as well, and should be kept in groups of 3 or more.
Perhaps pick 2 tetra types, and the danio. Or the gourami, a set of tetra and the danio. Or the gourami, and 2 sets of tetra. Or and all tetra tank. Or the gourami, a couple platy and a set of tetra. Platy do well in groups but aren't really schooling fish. Just be aware they are live bearers, so expect fry with a boy and girl or two girls. If you don't want fry, stick with males.
Try looking into either a school of 3 otto cats, a dwarf pleco or maybe a snail for the algae. Or in a tank that size, possibly consider saving yourself the space and scrub it yourself.
Best of Luck!

Take your tank... Clean it... and then put fresh water in it with a heater and a filter ( for tropicals ) Then I recommend putting these fish together
Serpae Tetra
Red Eye Tetra
Zebra Danio
L.F. Zebra Danio
Gourami

Id suggest at the MOST 4-5 fish for you are supposed to have 1-2 gallons for every fish...
Hope this helps.

Avoid the the gouramis and the chinese algae eater because the can become aggressive. The red serpae also can be fin nippy so be cautious. The rest can mix fine with 12 fish max. I would start over new, remember to take it slow start with a few fish and let your tank cycle.

Matry, I had a tank like this many years ago. Get about 6 zebras-they are a schooling fish and like to swim together. Get 2 algae eaters, AFTER you have some algae for them to eat. The tetras are small and stay small and you could get 4-6 of them. Also, a pair of Gourami's, two pair if they are small ones. Only 1 pair of 3-spots, as they are larger.

Put lots of plants in your tank, keeping room for the kids to swim and parade around.

Enjoy your fish.
Regards,
Dan