What causes low idle. If vacuum related how do I test it

What is your question?

Recently replaced the alternator on my 2005 matrix Toyota matrix started up normal and then they went to really low idle in our you can start it up in you have to keep your foot on the gas keep the idol up or else it will stall I also replace the radiator the same time that I replaced the alternator. Notice a little oil coming out of the top of the block. Last alternator was covered in oil

What makes this problem better or worse?

Only started when new parts where added