Shot schedule

You should take the enbrel on the same day every week to insure it is building up in your system.  If you miss a shot you can take  it the next day but any longer than that you will have to wait till the next week.   Yes you can take it with the meth, I used to when I was on it(meth).

It depends.  if you've been on Enbrel for longer then 2-3 months, it probably wouldn't matter as much as if you had just started taking the medication.  Once it's build up in your body, you may be able to play with the dosing schedule to work around things like bad days, having a big event you have to go to where you don't want to be experiencing the fatigue and queasiness that sometimes comes with taking Enbrel or methotrexate. Also, if you feel yourself getting sick, skip or delay your shot - as it suppresses your immune system even more, it's important to skip your immunosuppressant if you are getting a cold or flu as it can keep your harder time with a cold or flu or may also increase chances of complications. 

I'd recommend the next time you talk to your doctor, you bring a list of questions that you can develop over the next couple weeks - it's important that you and your doctor work as a team to make sure that you feel informed and safe in taking your medication.