Yes, I think that the TLVxx devices you mention are OK.
Yes, you can do something like what is shown in the PMP15039 design. Keep in mind that
thermals become important with such a small PCB; notice the thermal images in that document.
You can use…
I mean one wide input DC-DC + 2 to 3 converters for your multiple output rails. This would be an example of a two stage output: www.ti.com/.../PMP15039
If you need one chip, then you are looking at a PMIC. This site page will allow you to…