Would a coaxial cable splitter allow me to connect two cable boxes to one connection?

yeah the cable from the outside (where it comes into the house) you plug that into there but the more you split the signal the more it looses its power (look up dB loss to get a better understanding) but yes you can buy one and just run a cable from one of the jacks on the splitter

Yup. You can use splitter 

No problem to split the signal before the box. Newer broad band splitter and cable should be used (RG6F cable and 5-1002 MHZ splitter. type like that used for connecting old vcr or cable is unsuitable.) No need to pay for a second connection, there is plenty of signal strength to split it up to multiple units-using the correct wire and splitter.

Yes, but one thing that never mattered much in the past could be a problem now:  

Make sure the splitter is labelled as to passing signals up to or above 2 GHz. 

Some will be marked 2000 MHz, which is the same. 

You might get by with a 1GHz (1000 MHz) splitter on some cable systems. 

Yes, the only thing is you will be cutting the signal in half (even slightly less as the splitter has some loss + cable loss). This may not have any issue depending on factors but it good degrade the picture quality or it might make it so the cable box doesn't like it (doesn't get enough signal). This also depends on the type of cable box and such.

Best thing is to simply try it. My guess is that it will work fine for you.

yup, should work fine......

The older style cable boxes you can without any problem. 

Some of the newer ones that use the internet you may or may not be able to. It just depends. I would have to see how they're set up to give you a definitive answer.