The service feeders from the power co are 200a rated as is the can. The 150 CB limits the current going to the FP panel. This would allow the use of smaller wire to feed the bus bars. It does appear to be 200a rated so that is not necessary. The panels look to be in good shape. Nothing looks overloaded. So replacing it would be for a reason other than it's overloaded or in bad condition. Maybe you need more power due to a new AC unit or a house addition. Since I don't like FPE panels, that's all the reason I would want.
I would pull it all out. Go back with a 200a rated "Power Panel" which incorporates a meter base, a 200a main CB and bus bar space to handle up to 6 double pole breakers for "other stuff". It's all built into one nice neat can that mounts on the side of the house, run a stick of 2" rigid up through the roof with a boot, and slap the weather head (wasp house) on top and you're good to go.
This is what I have on my house. I reworked this a few years back when I built on a new addition.
You can feed the existing lighting panel from the power panel (PP) using a 4 wire cable. You can also pick up the HVAC loads as well as range and dryer from this PP. All would have to be 4 wire. I pulled the 3 I just spoke of out of my lighting panel and dropped them into the PP outside, as well as a totally new sub panel for the addition.
To answer the question about white wires on a breaker...... that would be old 240v circuits like water heaters and dryers and such. In the old days you could put the white of the multiwire on the breaker. Now days, it needs to be color coded other than white or grey to be on a breaker and not at ground/neutral potential... on both ends.
I don't work in electrical these days (I'm in low voltage security now) but I used to do a lot of electrical work and ran across the old Federal panels quite often. I don't like them. The breakers don't make very good connection to the bus bars. Parts are hard to get so I generally would replace them, and I think the other one I really hated was the Sylvania panels. The price I was quoted one time for 3 sylvania breakers was more than the cost of a new weatherproof Bryant panel with all the breakers to totally replace a panel...... so I replaced the panel.
As far as mixing Al & Cu wiring..... the bus bars and breakers are usually rated for either. It will state that on them somewhere or in the panel label. If using Al, which most people will do because of costs, using a rated "de-oxidation" compound is a requirement. Al also needs to be tightened properly. Loose AL connections will heat up and burn out. You do not want to splice Al wire to Cu wires. If you do, it's not advisable BUT, you can do it with a properly rated splitbolt..... best not to attempt this. Spring for wire that's long enough to reach without splicing.
If you are not familiar with electrical work, and or are not conversant on the current and existing codes and practices in your area, it would be best to have an electrician do the work or at least look at it before you call the inspector. Electrical work on the service entrance equipment needs to be done right and inspected.
A service change out can easily be accomplished in one day... 6 to 8 hrs or so.... including interior panel upgrade and new 4 wire feeder, but you have to have everything lined up, permits pulled, equipment on site, and all the tools needed to do the job, and a source of electricity other than your own house. I did that many a time by myself and always got the power back on before 5pm.