2005 Mazda 3 4 speed auto sedan noticed the AT and Engine light on

I watch your youtube vids but had to come send an email to you, for I have a few questions to ask/advice etc... Please answer all, for will help me ok. I urgently need this issue fixed/confirmed for I look after my 84-year-old mother by going to shops to buy food for her etc... and need my car running. Questions to follow...

Do you ship to Australia ?
If so to question 1, do you have Pay pal ?
My car is a 2005 Mazda 3 4 speed auto sedan BK. I was driving it the other week and noticed the AT and Engine light on, so came home right away and parked it. I then yesterday started it up but no AT light nor Engine light and all looked normal again, so went to shops "about 10min away". However, since owning the car (about 5 months), I notice is doesn't like changing at times from 2nd, to 3rd gear and now and then I have to put my foot down abit to make it happen. It also seems to stay in first abit to long before changing to 2nd. Lastly, the gear light on dash doesn't always show correct gear, for at time can be going from 2nd to 3rd but says I am already in 3rd or will be in 3rd but light says 4th. Then as I approach street lights and can be at an almost complete stop and shows I am in 3rd or 2nd, then once stopped says 1st, so seems like a delay. Can all I mentioned above, relate to that being the TCM ?.
If you don't deal with fixing/sending to Australia, can you advise me on how I can get this part and how to know if I am getting the right part for my car ? and to what price I maybe looking at?. I will be doing this job myself to help keep costs down, for electrician/mechanic will charge me too much. I am a battler, a real battler forced out of workforce due to health and Injuries but as said, look after my 84 yr old mother and NEED the car to work/be reliable, and need your help, can you ?.
Many thanks, for taking the time out to reply back, it is truly appreciated and, I look forward to reading your reply.