Grats on 50! To answer your questions:

1) Others have answered this in-depth, but in general try and get some sort of weapon upgrade (i.e. Ifrit book, Garuda book, etc.) so you'll have a decent weapon to use for Titan HM. Save up tomestones and get some Darklight gear (or get HQ Vanya made and melded if you are in a position to do so).

2) As others said, no caps really though there are apparently some diminishing returns...but I don't know if it's that significant. You'll be mostly aiming for Crit gear as a SCH (as opposed to spell speed and determination).

3) If you're looking to play SCH, I don't see why it's necessary to level another job to 50. Though as an Arcanist base class, you can also work on gearing up your SMN after your SCH gear is in place. This will give you an extremely viable DPS option for running content as SMN is highly desirable in endgame including Coil. As others mentioned, get cross-class abilities but prioritize Swiftcast as it's the most important. The only other cross-class that SCH can really make use of is stoneskin, but I would do that only if you have finished other things. Stoneskin is mostly useless for SCH, and even the situations in which you can use it it is not actually a requirement.

4) Both healers are essentially equally viable for all endgame content, at least in any sense that is worth talking about. The best healing duo is SCH+WHM by far, and both bring their own strengths to the table and synergize very well in 8-man content. SCH and WHM heal in different ways, but neither is truly better than the other for all situations, and both are required to perform equally-demanding healing roles in Coil.

Have fun!