A few pre-purchase Mini/MoCa questions

Hello, everyone. We have a Premiere XL4 and I want to connect it to a Mini in a bedroom. We have Verizon FIOS with a combination modem/router in an office on the lower level of the house. The Premiere is in the living room on the upper level (no ethernet nearby) and the bedroom is also upstairs (also no ethernet access).

If I have digested all the info I have read so far, we need to connect a MoCa adapter/bridge to the modem (downstairs) and then connect both the Premiere and Mini to coax (upstairs), plus add a PoE filter if we don’t already have one. Assuming I have that correct:

(1) The installation diagram talks about connecting the PoE filter to the point where the coax cable comes into your house. This is the same for FIOS, correct?

(2) Does it matter which PoE filter I buy?

(3) Should I buy the TiVo MoCa adapter/bridge or is some other adapter better?

(4) I don’t know how many/what brand of splitters we have in our house right now, but I saw a thread that recommended a particular brand of splitter. If I need to purchase a new splitter or replace any existing ones which brand is best? I thought it started with an “a”. Was it Antronix?

Thanks in advance for your help.