I have kept red cherry shrimps with pygmy cories with no problems. I have never kept anchor catfish so I can't say whether they'd be OK or not. But assuming you mean Hara jerdoni, I can't foresee any problems.
The sponge filter is ideal. The HOB filter - it depends. A lot of these have nothing but carbon cartridges in them. If the one you have acquired is like this, I'd go with the sponge filter. But if you decide to go with the HOB, I would get a block of sponge, cut a slit in it and push the uptake tube of the filter into it. This will stop baby/young shrimps getting sucked up.
Provided there are lots of hiding places the shrimps should be fine and breed. Newly hatched cherry shrimps are about 1 mm long and cream coloured. They need to be able to hide till they are bigger. And when you do a water change, check the old water very carefully. You will suck up shrimps of all sizes. Adults and juveniles will be easy to see. Babies won't be. When I had my 50 litre tank, I emptied the old water out of the bucket using a plastic jug- it was semi see through so I could see the tiny cream shrimplets in the jug. I used a pipette of the kind that come with fish medication to suck them out of the jug (I cut the end off to make it wider). Yes, it did make water changes longer than usual

Shrimps have a hard exoskeleton so they have to shed it as they grow. While the new 'skin' is hardening they are very vulnerable so they hide. Another reason to have lots of hiding places.
A few things that you probably already know but it is worth repeating them
Shrimps are more sensitive to ammonia and nitrite than fish are so make sure the tank is cycled before getting shrimp.
The shed skins look like hollowed out dead shrimps. Don't panic when you see your first

If you see the males whizzing round the tank they are looking for the female that has just released pheromones to say she is ready to mate.
Mature females have a light, saddle shaped patch on their backs. This is her ovaries filling with eggs.
Female shrimps carry their eggs between their swimmerets under their abodomens. It is called being berried because that's just what the eggs look like.