Mobil?... that's what is used in Holden racing cars! Fark that... Go for good ol' Shell and/or Penrite on the other side...
I put in 5 L 20W/50 Shell in my engine and a Valvoline Oil Filter. Does me good. Hey.. just drain out the oil, then take off the filter, replace a new oil filter back in, make sure it's tight... then pour in the new oil. Just don't pour in oil without the new filter on.
I don't know about transmission service... it is very hard to service it yourself. Take it to a transmission service mechanic and he'll check everything and he can even tell you what's wrong with it. $70 to $100 for full service... new pan gasket, seals and checking the band... most important.