I put my 2008 Rx400h on a four-point lift this past weekend for the first time. I could not find the oil filter. I've been changing my own oil and filters for more than thirty years. Am I becoming senile? Does it exist? Does anyone have a diagram?

no
not the pump
the distributor is installed incorrectly so do that again
ignition timing is 10 degrees BTDC max so any more advanced causes your problems
the noise is probably detonation form too far advanced ignition and lean mixture from the carby
suggest that you get a workshop manual for that engine and read on how to set it up properly

Looking under the car the oil filter is located just behind the front bumper, a little off to the passenger side. Should be one of the first things you see once you get past the bumper.
The link below has a very detailed step-by-step video of the entire oil change process, including locations of the oil drain plug and oil filter. Hope that helps.
2008 Ford Escape Oil Change - Detailed

well if u have never changed oil i would reccoment bringing it to someone to do it but anyways you will need a oil filter wrench an oil drain pan and some wrenches. 1st your going to have to jack up the front of the car fron the proper lift points and thn bring the oil drain pan with you and also take ur wreches. Look for the oil pan its mostlikely black and its going to be on the bottom of ur engin, thers a bolt in the bottom of it find the wrench for it losten the bolt and bring the drain pan under where the bolt it now take the bolt compleatly out and clean it off while the oil drains. onece it is drained put the bolt back in and make it a 1/2 turn past tight. now look on ur motor for some thing that looks like a small coffee can thats ur oil filter it twist off and be carefull because it is filled eith oil you also will have to dain this in the pan then clean off the area where the filter was connected then put on new filter and put oil into your car until the dip stick reads full..... good luck

Just like any other cars. The oil filter is located right behind the oil pan, they can drain at the same time. I usually put in 10 qts of oil with filter change, which does not reach all the way top of the max line on the dip stick.

If by flat spot you mean "hesitation" , you need to check the status of fuel filter, air filter and fuel pump. Inspect your spark plugs also as a precaution to eliminate them as the culprit.

the oil filter is a canisted type and is located under plastic engine cover lift the cover up on top of the motor and its on the driver side , it requires a 1 inch socket to change.

With a filter change along with the changing of oil. I would start with four quarts, than start the engine let it run for a second. After that turn it of check the oil, and top off as necessary. Roughly guessing I would say it holds about 4 1/4 quarts. Or could take up to five, its safe to start engine after four quarts. BE SURE to start engine after four quarts for 10-20 seconds, and then turn off to recheck. Too much oil can be catastrophic. (if no oil is showing on the dipstick than it is more than one quart low. The lowest point on dipstick represents one quart low, the middle is half a quart, and full is full) :)

you need a scan tool to do the job. either take it to the Lexus dealership or call up your local locksmiths, a lot of them can program remotes for less than the dealer.

You can almost always find some place like Goodyear, Firestone, Jiffy Lube or Midas advertising an oil change for just slightly more than you can buy the oil and filter. Why would you want to do this yourself? Especially since the first things you need are a jack capable of lifting the front of the car and some jack stands to support it while you are under there. You also need an oil filter wrench and common hand tools. If you don't already have these things, changing your own oil is not the way to save money Then there's the problem of something to catch the oil and where to dispose of it. But if you insist, once you get under there the drain plug will be at the lowest point on the engine. Take a look at the new filter, then look up from the bottom of the engine on either side, you'll see it.

Not unless you can reach it from the top. make sure you put some WD-40 on the bolts so they come off easy next time.