I do mixed-signal, which is mostly transistor-level design (analog), but also a lot of digital - both transistor-/gate-level and RTL.

I've mainly worked on RF transceivers for cellular, but eventually focused on ADC (analog to digital converters) IP that went into a variety of applications.

Pay depends on a lot of things - experience, type of circuit design, company, geography, etc. I've found that hardware engineer salaries on levels.fyi seem pretty accurate. IEEE also does a salary survey that you can pay to access for really detailed searches. You're definitely looking at starting salaries in 6 figures, and it's competitive with, but still below software engineers.

At small scales, I don't think it's profitable to do your own chip design. Many companies who start are just looking to get acquired rather than really sell their own chips.

Not really familiar with FPGA offerings sorry! It's a growing hobbyist area, though, so I'm sure you can find a lot of information on social media, youtube, etc.