Help, please! 7 weeks till triathalon and I need help!

This was my first year of competing in Sprints Tri's and like you I started with a plan.  Mine was 12 weeks long, but you should be able to complete the Tri with the eight week plan.  I think it is good that you are doing a shorter swim.  You should be able to complete the bike (yes your Mt. Bike is fine especially with road tires and it sounds like you have done some running as well).  The swim will be your biggest hurdle.  I found that I should have added at least one or two  more sessions each week in my swim for my first race.  I got through it but it wasn't the prettiest.  I did some side stroking and breast stroking during the swim as well; none the less, I finished.  I spent quite a bit of time looking at swim videos on line (YouTube and other links) focusing on freestyle technique and swim drills I could do each session that would add a bit of variety to the swim sessions and help me with swim technique.

I went a little bit beyond what an average first timer might buy for gear.  Some basic gear would be a good pair of swim googles (maybe a backup pair); ear plugs if you have balance issues coming out of the water (it helps); get a swim cap as you will probably have to wear one in the race so get used to it, sounds like you have running shoes, you might invest in a pair of Tri Shorts which you can wear on the bike and run (even the swim in some cases) or just compression shorts since the bike is 16 miles.  The Tri shorts have a little bit of padding on the bottom but not enough to interfer or inhibit your running in them.   

I am not sure of the temp of the lake you swim leg is in.  Some people rent wetsuits for the swim.  I did for my first two races.  I rented from Wetsuitrental.com.  Mybe a bit far and I am sure there are other vendors in the area to rent from.  The wetsuit will provide you some added boyuancy, floatation and warmth if the water is cold.  If you do decide to rent a wetsuit I would recommend you try it out in the lake two or threee times before using it.  It is a very different feeling wearing a wetsuit; otherwise just go without the wetsuit alot of people do this.  If you did wear a wetsuit you can wear your tri shorts and top underneath and not have to worry about putting them on in the First Transition (AKA T1; swim to bike).  Also go with another person if you are doing an Open Water Swim in the lake and if you haven't swam in Open Water Before make sure you stick close to shore.  It is a whole different swim than in a pool.

Practice riding without bike gloves as it saves you time in T1;  Very hard to put them on and take them off; if you feel you need the comfort and do not mind taking the time go ahead and wear them.  I had clipless bike pedals and bike shoes prior to starting triathlons so I used them as well, but those can be expensive so for your first one it is fine to just wear your running shoes.  Having your running shoes on will save you time in Transition 2 (AKA T2; Bike to Run).   Last few items for convienence - Race Belt to clip your Bib Number to for the run and possibly a timing chip leg band to attache you timing chip to.  I like the ones that are neoprene with velco better than the ones they give you at the races in your packet (reminds me of those bands they put on your wrist when you go to the hospital.

Again I learned alot wathcing videos of Transitions on YouTube.  It is amazing what you can find for assistance as well as looking around on BT which was a big help.

Lastly,  GOOD LUCK, HAVE FUN and ENJOY YOURSELF!!!