Already gotten good answers, but my 2cents anyway
1. A trainer can help you IF you find a good one who is willing to work with you. Don't pay for someone to tell you that you should go light or stick to machines (some trainers aren't as qualified and smart as others, ya know...). Otherwise, practice with lighter weights (I count those as warmup) until you feel comfortable maxing out.
2. I'm 5'2" and use the Oly bars... it may be a little harder for women / smaller people, but no reason to avoid them or be scared. Practice with JUST the bar at first, and always use clips to keep plates from sliding off when you do load it.
3. I use a squat rack (actually, it's a power rack at my gym) with bars that spot for me in case I get stuck. Don't need a spotter on DL, except maybe if you want someone to check your form.
4. Don't worry about what other people do. Do the workout all together as written, and make room for yourself when needed. Just because you haven't seen it done doesn't mean you're not perfectly correct in doing it.
5. HITT doesn't get "easier" because you keep increasing the difficulty. But, maybe you did too much too soon if you felt so awful... back off a bit or rest longer between intervals at first...