How do I replace the Stihl BR400 backpack leaf blower fuel pickup body and fuel line?

3 things you need for an engine to run.

Spark, Fuel, Compression.
Check you have all 3 and that they are GOOD. I suspect its a fueling issue, Either Its not getting to the carb or not getting to the cylinder.

replace your fuel lines first... you will need to remove the tank for this... then check to see if the carb is adjustable... if not replace it

Unless you are very handy, you might see if they sell the whole starter assembly, it would be faster.

located by the flywheel, held on by 2 screws. When setting the timing gap it should be 0.25 feeler guage.

are getting fuel

Oil leaking.? The only oil that would be in the machine would be the 2 stroke mixed in the fuel.. I dont understand where 'oil' would be leaking from. (more info please)

Also your question refers to an 'older homelite weedeater' yet its titled 'Problem with Stihl BR400 Backpack Leaf Blower' Which one is it.?

I would say it is not an issue with the piston and rings, any oil leaking from the muffler has to be unburnt oil from the fuel/oil mix, if not already you should run it at a 50-1 mix, also make sure the engine is not running too rich on the fuel screws, check the condition of the air filter as a blocked filter will richen the mixture.

The oil to gas ratio is off - you need to either dump the fuel or run all the fuel out of the unit clean the carb and tank - replace the plug and filter mix gas and oil to correct ratio start and let run for 10 to 15 minutes - your carb may need to be adjusted as well.

check the shire pin on the flywheel and also check your on/off switch

http://www.stihlusa.com/stihl_ownersmanuals/br340_420_manual.pdf