Possible reasons could be
Shravan is supposed to be the holiest month of the Hindu calendar. It is full of festivals and minor celebrations. Festivals include Janmastmi, Raksha Bandhan, Naag Panchami, Onam, Kajori Purnima, etc.
Shravan is the holy month of Lord Shiva. Every Monday (day of week dedicated to Lord Shiva) is called Shravan Somvar. All the 4 Shravan Somvars are special and you are supposed to be fasting for them. As Shiva's chosen month, every day of this month is laden with religious significance, so Hindus avoid non vegetarian food and liquor in this month.
This is the month in which the monsoons are in full blast. The rains bring a whole lot of water borne diseases with them. The general hygiene is bad and you never know what infection you might catch. Hindus believe that meat during this month has more chances of being infected. So it is better to avoid meat.
Shravan in mythological terms is the month of love and romance. Practically it is the breeding season for most of the animals. Fishing during this time is prohibited by Hindu laws as the female fish have eggs in their stomach. It is a sin to kill animals when they are pregnant or hatching eggs. That is why Hindus avoid meat and fish during this month.
However, I don't know the relation of not shaving in Shravan Maas.
As shared by @Rishi Kulshreshtha, Shaving is not done in Shravan Maas because during that time, the Straight razor use to get infected by rust due to monsoon and it can cause skin injuries. Refer straight razor