The Questioner himself has listed certain days on which one must not shave. Looking at this in its entirety:
Months:
The four months of Adi, Margazhi, Maci and Purattasi. During entire month of Purattasi one must avoid shaving
One can shave during the first half of the month of Adi and must not shave during the second half
It is said that one must not shave during the first half of Margazhi and Maci; shaving is allowed during second half of these months.
Days:
Shaving must be avoided on Tuesday, Fridays and Saturdays
As Fridays are not suitable for one’s mother, some with no mothers will shave on Fridays.
Tithi:
One must not shave on Pitru tithis – Krishna paksha Ashtami, Krishna paksha Caturdasi, Amavasyai, Paurnami. Generally people avoid shaving on Chaturthis. All Sashti tithis must be avoided.
Nakshatrams:
One must not shave on Bharani and Krithikkai as these starts are considered auspicious (Mangalam). A few do not shave on their birth stars.
Mondays and Wednesdays are days when one can shave even when these days are afflicted with certain shortcomings or defects