Best way to power a microcontroller, SMPS vs Linear Regulator
1) Buck converter is:


more expensive than a linear regulator
takes typically more room on the PCB
is typically more difficult to design (sometimes, just a bit more, sometimes way way more)
is more noisy (the amount of noise depends on a lot of factors, though)


But it is indeed much more power efficient, especially if there is a big difference in the input voltage vs output voltage, which is your case here. The buck will output almost the same power than it takes at the input (efficiencies are typically ~80-90%), whereas the linear regulator will take as much current as input as it needs to supply (which means that efficiency is Vout/Vin, something like ~27-44% in your case, which is very bad).

2) Yes, this is actually the only reason why linear regulator can be a bad choice: the efficency (and your computation of dissipated heat is fine). Now, having that much power dissipated leads to two big problems:


You will probably need a heatsink (check the datasheet of the linear regulator: at anything more than 1W, you need to check carefully even in TO-220 package. When using smaller packages, it is often not possible at all). So this negates the "more room on PCB" inconvenient of buck regulators.
If you run on batteries, it means much less runtime. Sometimes, you can't afford it (do the computation).


3) Most likely not, if you use standard integrated solutions to do the stepping down. Those are made to provide power to IC chips, and the datasheet/application notes of the step-down controller/regulator you'll choose should give you some information about the amount of noise you'll get. But for digital operation, supply noise isn't typically that much of a problem.

4) Given the huge difference in input/output voltages, the current you need, and the fact you'll partly run on batteries, it seems a logical choice to go for a buck. But you need to double-check all that yourself. Maybe in your case it is acceptable to have a huge TO-220 dissipating 1.3W in your enclosure, and the runtime you need isn't that high.

If you go for a buck, here is what I can suggest:


One solution is to go for a complete module. You then don't need to design anything. Check mouser/digikey, they have DC-DC converters that you can just solder to your PCB like a linear regulator. If you're an aliexpress/ebay kind of guy, you'll probably find plenty of cheap things there also.
You can design your own (scary, I know... wow, an inductor!). What I can suggest in this case is to have a look at the tools provided by the various manufacturers (e.g. TI webench, but Linear technology has one too, ...). You just supply them with your requirements (input/output voltage, current, ...) and it spits out a lot of possible designs (you'll see some of them are actually very simple) with different chips from their catalog. All the passive component values are already calculated for you, and they even suggest you part numbers for the inductor, etc... So you just have to check the recommended PCB layout from the documentation to design your board, buy the parts, solder, and it should work.