Regarding your mortgage supplement - not all of your earnings will be assessed against you.
The first 75 euro of your earnings will be disregarded.
25% of the remaining earnings will be disregarded.
JA assess part time earnings as follows.
You are allowed to earn 20 euro per day up to a maximum of 3 days per week.
60% of the remainder is assessed as means, and will be subtracted from your full rate JA.
This link explains the means test in a bit more detail
Means Test for Jobseeker's Allowance
If you've been unemployed and in receipt of JB or JA for 12 months or more, and take up part-time work, you can retain your medical card for 3 years from the date that your income exceeds the medical card guidelines. If you have been in receipt of JB or JA for less than 12 months, your medical card will have to be reviewed to determine continued entitlement.
Other AAMers may have advice on the proposed method of payment for your work - it sounds as if you're being treated as a sub-contractor, responsible for your own Tax, PRSI, etc...