The alternator died- replaced the alternator, replaced the thermostat housing gasket, changed the battery, changed the oil, topped fluids and took the car for a short test drive. It lighted 'Restricted Performance' and then smelled funny, and when I opened the hood smoke is coming from the driver's side of my engine. Nothing like this was happening before I changed the alternator. It is also idling just a little rough- barely.
Any idea what is going on?

Is there any check engine light codes aside from restricted performance?

What does the smoke smell like, and what color is it? Is there any visible leaks, especially at points where parts were changed recently. Be sure to look in the valley and around the injectors, spots where water could pool without being obvious. Any fluid spots under the car?

On the alternator, is the voltage the new alt/batt have when the car is running, close to 14.4v?

You changed a lot of things here. Let's isolate them.

Check voltage when car is running. Mine runs @ 14.2 at idle with nothing on.

What does the smoke smell like?
Oil?
Coolant.

If oil, did you tighten the cap and not spill any on the exhaust?

If coolant, did you replace all the coolant?
When changing the thermostat housing, coolant can collect in the valley of the engine.
What temp is it running at? Mine runs @ 186 degrees @ idle when warm
Did you re-tighten and check the hoses for leaks?

Did you replace the hoses on the housing correctly? These hoses can break easily.

Did you damage/remove any of the coolant lines that run along the valve cover? These can break very easily. I know from experience.

Did you remove any vacuum hoses?

Lastly, what codes are you getting from OBD?

Check to make sure the serpentine belt has been replaced correctly on all pulleys. It's easier than you think to install the belt with one rib hanging off the A/C pulley and shred a brand-new belt. Don't ask me how I know this.

I checked the belt, and it's correct.
We don't have a code reader yet, or a way to check the battery voltage. New to repairs.
But the radiator fans, neither one of them is going at all. The fuse is fine.
Also, the smoke I think was from the valley and it was coolant smoke.

The fans are now running.
Voltage is running at 14.5, and we got our code reader in. It is coding:
P0332 knock sensor 2 circuit low input
p1111 system pass (?)

the abs certified system recommended changing the knock sensors and the intake manifold gasket on all 8 cylinders. It said replace knock sensor and wiring harness as well.

Reset the knock sensor code and see if it comes back. I know from experience that this code can be triggered by the exact problem you described about coolant in the intake well. The knock sensor and coolant don't mix real well.

You need to drive the car a couple of hundred miles and the P1111 will go away. This code means it's running its tests. The catalyst test takes the longest.

+1 on resetting the code. The knock sensor will activate just from washing off the engine. Doesn't take much to short them out. If your lucky it will dry out and be OK.

Another +1 on the resetting first, and have a try.

However, the P1111 will not go away, and is the only code you will want to see on a Jaguar.
It means all systems have passed their check after the last clearing of codes.
It will start with a P1000 code after clearing, then changes to a permanent P1111 after all is done, that is until you clear all codes the next time.

we tested the knock sensors with a multimeter and one side reads 180k ohms and the left side reads 54k ohms so I am wondering if one is damaged- would it do that if it was just wet? Or should I just assume it is damaged?

I think it is because they are still wet. Try spraying each with electronic cleaner: helps dry them out and cleans residue from coolant. At the worse, not that hard to replace -- if you are careful (plenty of threads discuss this issue, even a YouTube if memory serves).

And Eric is correct, RPACH has it backwards: P1111 is the only code you want to have and must have to pass emission tests in many locales.