The first one could be MAF or CAT related... obviously over fuelling for some reason.
The second one... it's a bit vague from that description, but could be relating to the alarm interior sensors. What error code did it bring up? Get that and look it up in the VAG-COM forum section as I'm sure it will have been discussed before.
Need the numbers that go with the errors to be honest, but the "Fuel Trim too Rich" is probably your coolant temp sensor - common problem try a search.
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