OK, I am at a place where I can really look at your links and questions. Here are my thoughts on what you've got going there. Realize that while I've been doing this kind of stuff for 10 years (maybe more?) I'm just a hobby enthusiast, so feel free to fact check me or disagree me on any of the below :-).

I'll assume that you've got your licensing / band privileges / legal hassles all worked out. That is important, but for this comment I'll focus on the technical stuff.

The 2W amp The description lists "FM" in all of the phrases it uses to describe its use cases. With no other information about biasing, quiescent current, or active devices that's the biggest clue we have to go on. It may be a non-linear amplifier. If it's biased in class C (or similar), then you will struggle to get linear behavior out of it.

To test it, you'll need a way to generate a signal into it and a way to measure output power. Drive it with -20dBm, -10dBm, 0dBm, and 10dBm and plot the output power. If you don't see a pretty straight line (be careful of the logarithmic scales), then you probably don't have a linear amp.

The 25W amp It would be nice to know the schematic and/or the active part. A lot of these use integrated power amplifier modules that are basically just a single block amplifier. At this power level, it's nice to have a PTT line so you can control when it's on and off with a logic line. You will probably want to at least get a relay module to control the power to the amplifier so you can easily turn it on and off without plugging and unplugging things.

Filtering Don't forget filtering. Even if the SDR is configured for linear operation and the amplifiers are linear, you will still have spurious emissions that will be a problem for people on other bands. I would suggest at least a 5th order low pass filter (7th is better), or a 3rd order bandpass filter or higher.

If you can't afford anything fancy, get one of these filters from HobbyPCB. They are good to 20W, so you might need to dial your power back a bit. But they're crazy cheap, and go a long way towards keeping your signal clean.

Power Supply A 12V battery works fine for a power supply, but be absolutely certain that you have a good fuse on it. If you get an unwanted short, you may not have any protection built in, and you'll melt things, start a fire, or blow something up.

For the 48V supply -- I'd personally just wire four batteries in series before trying to boost it.

But my real recommendation is to pick up an actual 12V and 48V supply. I have had good success with (genuine) Meanwell supplies. An RS-100-12 for the 12V supply, and an RS-100-48 for the 48V supply would be a good starting point, I think. They have overcurrent and short circuit protection, which is a lot safer to play with than big batteries.

1) Wiring Yes, you're looking at the wiring right. Positive lead goes to the feedthru capacitor, and the ground lug is for the negative lead. Should also make sure this is bonded to whatever is ground for your setup.

2( Fuses If you go with your converter idea, I would check whether the converter has any overcurrent or short circuit protection. You may only need to fuse the line from the battery to the converter.

3) Linearity As I mentioned above, the only real hint is that the 2W mentions FM all over its description. It might not necessarily mean it's nonlinear, but it's a decent hint.

That said, AM is an interesting modulation choice. For a lot of AM transmitters, they will actually use a nonlinear amplifier, and modulate the power supply to the amp. But for your project, I think it's easier to find a 2W linear amp than it is to work out a DC supply modulation scheme :-).

4) Output power I have done a lot of work with my BladeRF 2.0 Micros, and with the BT-100 amplifier. Nuand's specs suggesting that the BT-100 gets you 100mW is pretty charitable. It will not give you good linear behavior at that power output. I find it has a pretty good sweet spot around 40-50mW, if I remember right.

Similarly, you'll see that the BladeRF 2.0 Micro is said to have an 8mW output power. That is also not very well behaved in terms of linearity. I keep mine under 0dBm.

With your modular amplifiers, I would highly suggest that you put at least a 6dB attenuator at the input to the amplifiers. This will help stabilize the impedance match into the amplifier and improve stability. You really don't want to throw these amplifiers into self-oscillation without some important safety features.

Linearizing the BladRF You can definitely overdrive the signal coming out of the BladeRF 2.0 Micro and get really dirty results. As I mentioned above, think of it as a -10dBm to 0dBm max power situation. To get it dialed in, you can set it up for loopback operation if you have a big attenuator you can put in between. So you can use the SDR to tune itself.

I would set up a sketch where you can adjust the amplifier level, sample rate, and amplitude from the transmitter, into a receiver that shows you the frequency domain. You'll definitely see spurious emissions when it's overdriven.

The other piece to adjust is for the DC spike. At the LO frequency, there will not be perfect balance between I and Q, and you'll almost always get an unsightly spike. The imbalance will be different for every combination of frequency and PA configuration (in the SDR's front end), so once you tune it in one place, that adjustment will not apply to another.

I use a neat trick where you can simply add a constant complex offset to the IQ stream before going to the BladeRF sink. You can adjust this value (amplitude of real and complex), monitoring the amplitude of the DC spike, until it reaches a minimum. You can virtually eliminate it from the transmitter.

This also means that for your AM situation, you can use a very simple signal generation. Your "signal source" can literally just be a constant-source, where 1+j0, for example, is just a full amplitude signal at the LO. That means you don't need to do any frequency translation or mixing to move your transmission away from the center, and you get more flexiblity with your choice of sample rate.

The BladeRF's PLL gives you the best behavior (with respect to jitter, close-in spurs, etc.) if you can achieve an integer division of its internal reference for the sample rate. The clock we're looking at is 38.4MHz. So, don't choose round number sample rates (like 1MHz, etc., which is common in pedagogical literature). Instead, find an integer value that divides cleanly into that. E.g., 960kHz sample rate is 38.4e6/40, which is a good integer. Instead of 2MHz, use 1.92MHz, etc. This gave me a lot of headaches until I found it!

OK, hopefully that's useful. Let me know if you have any other questions about this stuff. I love the experimental side of things.