New alternator needed?

[perx]

Hello everyone happy Saturday hope all is good.
I own a e92 m3 dct 2011 lately car has been very bouncy on voltage some days I’ll be driving on 11.50 volts some days 14.80 seen it 15 at one point some morning idle would be at a solid 900 and doesn’t go down till I start driving the car I know about the warm up process but even when car is warmed it’ll still idle at 900 but when I drive and I come to stops the car will be around 600-700 my door lights will flash rapidly and and sometimes when I use the paddles the car will double up shift like from 3rd to 5th right when it changes to 4th so I’m thinking could it be the alternator I checked all fuses and grounds all looks good I do have homemade copper wire ground at the back of the exhaust because I am cheap and I don’t wanna buy a $50 oem ground strap sometimes I do get battery discharge message but only once in a blue moon battery is only a month old as well so I don’t think it’s the battery let me know what you guys think it could be. Sorry for the run off sentence.