There is nothing inherent about a Synchro Monster that stops it being used as the Synchro Component for another Synchro Summon. So you could freely use Ally of Justice Catastor and a Lv 1 Tuner for...
No, not unless the Synchro Monster actually says it is, like Formula Synchron, which is both a Synchro and a Tuner. Normally though they are just Synchros.
Synchro Monsters are the newest type of Monster Card. Their color frame is white and include "/Synchro" next to their Monster Type. They are included in the Extra Deck (formally known as the Fusion...
As long as the Synhro Monster can be reborn, and was summoned correctly, then there is no strict limit, you can keep resummoning it as long as you have cards or effects that can do so.