the fuel sending units ar under recall for corrosion on the connector, check that, pop the wires, cap and rotor off the distributor and check down the hole revealed by removing the rotor for dust or metal shavings if found you need a new distributor, common as these trucks get miles and age.

check the fuel pressure regulator is not leaking, it is mounted under the intake manifold (upper) its a bit of a hassle to change but cheap for parts if its bad it can cause poor acceleration and fuel economy as well as exhaust smoke from unburned fuel and poor mpg which the 1st gens have already but if you srent getting around 14-15mpg mixed hwy and city you need to check that. if oil is leaking from the passenger valve cover this can make the exhaust smoke and mimic a rear main seal issue have a code reader hooked to it (even if the check engine light is not on) as the previous owner may have reset the ecu to get it sold, if you see a p0325 or 328 code and yours does not have a supercharger feel free to ignore these they are knock sensor codes and do nothing to make the truck run worse nor fail emissions. Satito might chime in and add some more he has alot of 1st gen knowledge as well and might have some more to add.

 

The white smoke from under the hood could very easily be just the remaining oil from the VC gaskets leak burning off. Keep an eye out to make sure it doesn't start leaking again. Some times a sneaky mechanic will just torque the bolts down to stop the leak, but that's a temporary fix at best and it always starts leaking again because the gasket is brittle and cracked. It is also possible for the gasket to be twisted or to come out of the "track" during reassembly, which will also cause it to leak. So just keep an eye on it.

An easy check for the FPR is to simply pull the small vacuum line attached to the back of the intake manifold off with the engine running. If any gas comes out of the hose, the FPR has a bad diaphragm and is squirting unmetered fuel into the intake. This can cause black smoke out the tail pipe, carbon on the #6 plug, a #6 misfire followed by a random misfire code, and poor acceleration etc.

As far as the steering leak goes... Where is it? The hoses leading to the reservoir are well known to go bad and leak, but the good news is that they are super easy to change. it does mean that you lose the fluid in the reservoir, so make sure you have some automatic transmission fluid to refill it after (I like Valvoline MaxLife). The power steering in these vehicles uses automatic transmission fluid (it should be red in color). Get the aftermarket hoses from Rock Auto if you want to save some cash, or an online Nissan parts store like Coutesy Nissan if you want OEM. If the leak is coming from the bottom of the steering gear, then you simply need a new pitman seal on the steering gear ($10-$20 from RockAuto) in parts and about a half hour of work if you've done it before an hour and s half for a first timer (I've replace them on both my 2000 frontier and 2003 Xterra. It's very common with age. Do not let a mechanic talk you into installing a new steering gear because of a little leak.
It's an expensive part and totally unnecessary. The seal can be replaced with the gear still on the vehicle.

I would get the codes read to make sure nothing has come up. As kms1990 said, the knock sensor can more or less be ignored on the normally aspirated model, though if you have a reason to take the intake manifold off it is worth fixing while you are in there.

Feel free to ask any questions and keep us updated. If you decide to do some of the work yourself we are happy to give tips and also point you in the direction of decent YouTube tutorials. Remember that many specialty tools can be borrowed from Pepboys, AutoZone etc under their tool loan program, do DIY work doesn't have to break the bank paying for tools you'll only use once.

 

Also...
You may want to replace the fuel filter. It's possible that it's still got the original filter and there's no telling if the vehicles sat for any length of time, been filled with dirty or bad gas or has had water/condensation in the tank. All of these things will cause a filter to clog and result in poor performance.

Fuel filters are cheap and really easy to change on the gen1. You should be able to get the filter for about $15.

 

Lots of good information here. I'll put in my 2 cents here as well if I may .

As previously stated, the white smoke under the hood is probably oil burning off the exhaust from the Valve Cover Gasket(s) leaking onto them. Depending on which Valve Cover Gasket is leaking, you have some options. I'd recommend changing both of them just to get them out of the way, but if it's just the passenger side gasket leaking, that one is pretty easy on the first generations (I believe you bought a decent truck. If you would have bought a 2nd generation, 2005+, then I'd be meh about it, but the first generations are great based on my experience so far). Not much is required to change the passenger side. Now if it is the driver side, you'll need to remove the upper intake, which, as a beginner DIYer, I didn't have that much of a problem, except for the coolant lines hiding in the back. This is where the previous comments come in handy for changing the Fuel Pressure Regulator. Highly recommend changing it while you're in there because that is when it is the easiest to change.

I'd also change the fuel pump if it's original as well. Mine went out about that same mileage too, and if you take it to a shop for that, I believe they're required to change the fuel filter as well. But if not, get that service done, too. My symptoms were hard starting, and eventually came to a crank, no start situation.

However, a weak fuel pump and/or a clogged fuel filter can cause accelerating problems, but A LOT of things can cause that symptom. So my advice, give your X a basic "tune up" if you aren't sure of the history. I'm not sure what your mechanic went over, but I would change the spark plugs, check the wires to make sure they're still good, inspect the air filter, check all fluids - might look into the Transmission fluid to make sure it's still a good color (bright red/pink) and doesn't smell too foul or burnt, clean out the throttle body, and all that good stuff. If after doing most of these things doesn't help the accelerating issue, it would need to be looked into a bit deeper, but don't forget about the basics, they're usually cheaper, you can do it yourself, and then at least you don't have to worry about them for a long while .