They're not going to be in phase. Note that if phase relationship is important, at those frequencies cable length being identical is rather important. But its not relevant to this problem.

One big confusion in the electrical world is people use the same noun for audio "mixers" which are as linear as possible, and RF "mixers" which are as non-linear as possible. They do different things. linear mixers you could say superimpose signals without changing them. Much like pumping up the gain on a CD should not distort the sound on a mic at a "DJ" mixer. nonlinear mixers add and subtract signal frequencies from each other and what came in shouldn't come out at all. in fact a BPSK mod is a kind of balanced mixer, with peculiar TTL compatible (or 3.3v or whatever) levels of course.

You want a 4-port combiner. Most passives have a reciprocal path, a 4-port splitter usually makes a decent 4-port combiner. Think of the gadget that probably splits you cable TV signal in your house. They're electrically and mechanically simple. And relatively cheap. Also they are somewhat lossy. Good luck passively splitting a signal 4 ways with less than 6 dB of loss. And something is warming the resistors in there, so its going to be worse. Conversely yes you combine multiple signals there will be internal loss but the aggregate output will be higher. This is kind of the whole point of a class B or class AB amplifier... what if you took two perfectly good signals, 180 degrees out of phase, and (sorta) mixed them (using baluns), well you get very near twice the power out. Think of putting the whole works in a calorimeter... 4 zero dBm sources will heat it up just as fast combined or separate.

Aviation GPS "around 1.5 GHz" works pretty well despite being feet/inches away from a couple watt radar transponder around 1090 MHz or whatever it is exactly for ADS-B. Physically zorching it sounds unlikely. Distortion to the point of un demod ability is however possible. If you generate enough signal to overload it, attenuators are cheap. High power is expensive. If you're screwing around at "workbench range" you're not going to pay $XXX to generate multiple watts of power so you're not going to need multiple watt rated attenuators to reduce the sig level to something reasonable. Cost scales WAY beyond quadratically, like exponential at microwave freqs for a given tech type. Stuff working around a hundredth of a watt aka 10 dBm is going to be very cheap compared to stuff rated for old fashioned weather radars at kilowatts.

My suggestion is make what amounts to exactly one working satellite. Then make three more.

I don't think you can feed all four digital signals into the same BPSK mod by doing weird things with the clock rate, modulation does not work that way.

What you're building is vaguely reminiscent of a cable TV headend. Both in block diagram and actual wiring. Of course its been a long time since BPSK was cutting edge in CATV. If you think of BPSK as no amplitude modulation and either 180 or 0 degree phase modulation depending on 0 or 1 being input, well, a 256QAM signal is just 16 equally spaced levels of amplitude modulation and 16 equally spaced levels of phase modulation, sorta kinda a grown up cousin of the BPSK modulation in GPS signals. And 256QAM is sort of cutting edge for CATV. Anyway you could do worse than looking at a wiring diagram of a CATV headend WRT mods and digital sources and combiners and such.

Find your local ham radio VHF/UHF microwave club / community. Don't bother with the 160meter low band guys (well, not for this particular individual project, I mean) By the time you're done you'll know quite a bit about RF and might gain a new interesting hobby. Reading several "microwave handbook/project" ham radio books at the library would probably be as good a place to start as any. You could do worse than some chapters of the ARRL handbook to start.

Analog is fun. People will tell you the world is digital, but even their digital ckts are fundamentally analog. And if analog is fun, RF is just magic. A craft not a science at the higher levels.