Welcome very, I’ll try and answer your points!
800 cals - I aim for approx 800 but once I’ve worked it all out it’s usually 900-1000 cals. Keep the carbs low, but there’s no hard and fast rule to keep under 50g. The key is eat a variety of the allowed foods, and you’ll be ok. If you’re tdee is higher you could probably allow an increased amount of cals. I’ve always found 1000 I would still lose, and it was more sustainable long term. The 800 cals is specifically to burn away the visceral fat around the organs to increase insulin function in T2 diabetics. If this doesn’t apply to you then there’s no real need to strictly adhere to 800 cals a day.
Loo- (tmi warning!) Constipation is consistency rather than frequency- so you may not be constipated as such, just going less frequently as you’re eating less food. Bloating could be caused by a high intake of lentils, pulses etc? You can try things like psyllium, chia seeds, to help things along? Check the fibre in your diet - you should be aiming for approx 14g per 1000 cals of food as a guide, so about 10g per day.
Dry - from what you’ve said in your post, my instant thoughts would be that you may not be eating enough fat. This may not be correct so forgive me if I’ve jumped to a wrong conclusion, but all 3 of your queries could be attributed to not consuming enough fat- ie, feeling hungry at 800 cals, toilet issues, and feeling dry/ dehydrated.
Is this your first time on BSD? Have you done other, conventional diets? (Ie sw or ww?) - I found it very hard at first to switch from the sw mentality of loads of low fat food, to this plan with its tiny portions, and I could ‘feel’ the fat in me when I ate. But over time we get used to it. Fat is your friend on BSD so based on your post that would be the first thing I’d look at and see if that helped.