Mechanical filtration:
Many people use mechanical filtration (most common being filter socks in sump) but its just personal preference. When I had HOB filter in my 20 gallon reef, I used a sponge in it. But when I moved to 70 gallon with sump, the mechanical barrier caused problems with water level in the sump so I removed it. Sponges/floss/filter socks just add a layer of extra source of removing detritus but also adds a very strict maintenance schedule (clean every 2/3 days). About the pieces of live rock, many people use it in sump/filters just like ceramic blocks. Gives greater surface area for bacteria to grow and work.
Protein skimmer:
Possibly the most debated topic in salty side. It all depends on what sort of tank you tank and how often you are ready to do water change. For my 20 gallon, I didn't use protein skimmer for like 6 months till I started noticing that my water change was not keeping up the health of the system (it had 50+ corals and 8 fishes) so I added a skimmer. There are many systems, both big and small, which don't use skimmer and are equally beautiful. If you want to put a skimmer in your 35 gallon, I would say go for AquaC remora or reef octopus. Deltec are the best but are extremely expensive.
Water:
Some people say RODI is a MUST but not necessarily. Its just that tap water has a very high variability from season to season. Its not just the phosphate that can feed algae but many other sources, like silicate. RODI just makes sure that nothing bad gets into the water. Its not a mandatory thing (again, I ran my 20 gallon using tap water) but its just an insurance.
Mandarines need food almost whole day. Many can get them to eat frozen food but again, they make sure that food is almost always available to them. Captive bred are very expensive. If you really want one, start the tank, add pods, wait for 6 months or something, see if you have pods all over the tank, go to LFS and see if the mandarine eats frozen and buy. Its not impossible but its hard.