Mouth guard applied H2O2
These shouldn't be performed at home, and only with a trained nurse or dentist (not a cosmetician).
"The British Dental Association warns anyone who isn't a nurse or dentist won't have the right training or knowledge and could cause permanent damage to your teeth and gums. For example, if the mouthguard containing the bleaching gel does not fit properly some of it may leak and cause painful chemical burns. In extreme cases, people have been sick after swallowing the bleaching product." (https://www.bbc.co.uk/news/health-34257444)
What % is most effective to use for home gel peroxide kits?
There was no difference in the number of shades of whitening at 6 months when 35% H2O2 was compared to using 6% H2O2 - https://pubmed.ncbi.nlm.nih.gov/25799793-teeth-whitening-with-6-hydrogen-peroxide-vs-35-hydrogen-peroxide-a-comparative-controlled-study/.
How long to leave peroxide gel on for?
"These results indicate first that the number of bleaching treatments can be dramatically decreased, which is consistent with a study by Polydorou and others21 showing that a bleaching time of approximately 24 minutes is sufficient to reach a clinically significant level of bleaching" - https://www.jopdentonline.org/doi/full/10.2341/15-010-L
Doing many 1+ hour long applications can weaken enamel, but less than 5 x 30 minute applications in a short period of time did not harm enamel or tooth hardness measures - https://www.jopdentonline.org/doi/full/10.2341/15-010-L
Is putting hydrogen peroxide in your mouth safe?
In a 2006 review it was concluded "There is no evidence of preneoplastic or neoplastic lesion development in humans for hydrogen peroxide tooth whitening products" - https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1708-8240.2006.00006.x
There is evidence of some cancer causing activity in very high long timeframe doses in animals, but the aforementioned human data seems to trump this: "Potential health concerns related to prolonged hydrogen peroxide use have been raised, based on animal studies. From a single study using the hamster cheek pouch model, 30% H2O2 was referred to as a cocarcinogen in the oral mucosa. This (and later) studies have shown that at 3% or less, no cocarcinogenic activity or adverse effects were observed in the hamster cheek pouch following lengthy exposure to H2O2" - https://pubmed.ncbi.nlm.nih.gov/7500245-hydrogen-peroxide-a-review-of-its-use-in-dentistry/
40% of people had tooth sensitivity in a 45 minute application of 15% H2O2, whilst 90% of people did when 35% H2O2 was used in a randomised controlled trial, but similar efficacy on whitening was shown - https://www.sciencedirect.com/science/article/pii/S0300571217302841?via%3Dihub
The lowest % concentration possible, with minimum of 1 - 3 %, for the shortest time possible should generally be aimed to be used to minimise tooth sensitivity.
Damage to gums?
It appears to actually increase gum health by acting as an anti-bacterial/anti-yeast/anti-viral.
In this randomised controlled trial: "The adjunctive use of hydrogen peroxide to chlorhexidine proved to be superior to chlorhexidine alone with regard to the inhibition of plaque and development of stains." - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3800406/
"Studies in which 3% H2O2 or less were used daily for up to 6 years showed occasional transitory irritant effects only in a small number of subjects with preexisting ulceration, or when high levels of salt solutions were concurrently administered" - https://pubmed.ncbi.nlm.nih.gov/7500245-hydrogen-peroxide-a-review-of-its-use-in-dentistry/
"Furthermore, wound healing following gingival surgery was enhanced due to the antimicrobial effects of topically administered hydrogen peroxide. For most subjects, beneficial effects were seen with H2O2 levels above 1%." - https://pubmed.ncbi.nlm.nih.gov/7500245-hydrogen-peroxide-a-review-of-its-use-in-dentistry/
Is it prescription only?
This BBC article (https://www.bbc.co.uk/news/health-34257444) state that 0.1% H2O2 is legal in UK to be sold over the counter, but dentists can prescribe up to maximum 6% concentration home kits via teledentistry or in-person consults.