I'm more than happy with the questions! I'll try and answer some of them.
Mary is, indeed, a bit of a mystery. It has always annoyed me that I can't find her baptism as it would nail her year of birth, possibly, and clear things up.
A lot of the answers to your questions are on the various certificates. For years, for instance, I despaired of finding out anything at all about Jane Parkman who married George Serjeant because her marriage certificate shows no father and her baptism record at St. Pancras church shows clearly that she was illegitimate and that Mary Parkman was her mother. The marriage cert interested me because it had two names on it as witnesses that meant nothing to me. Then, years later, ta daaaa!! I discovered who they were. The woman (Eliza Jane Heald) was her first cousin, daughter of Amelia Parkman Heald, one of Mary Parkman's sisters. The other person, Benjamin Turner, was her uncle, married to another of Mary's sisters, Jane Blandford Parkman. (The Blandford in this case is taken from her mother's maiden name.)
On Philip's death cert, the death is notified by his married sister, the Amelia Heald mentioned above. He was living at 50 Johnson Street, as was Mary, her widowed mother Jane, Jane junior who was 17 at the time and Fred, 13. I do take your point about 'seaman' on the census, but then again maybe the census taker wasn't that interested in the finer points of marine heirarchy! And he is referred to as a 'Gentleman' on the death cert, which I would think points more towards a retired Master than an oick sailor, wouldn't you?
Frederick is another one. Shown as born in about 1829. Now, Jane was born in 1825 but not baptised until St. Pancras in 1830. So, why was Fred not christened at the same time, I wonder? They often did job lots, in my experience. Was he not there at the time? It gets better. I couldn't find him anywhere else until someone on a Scavenger Hunt helped me and he was located as living (called 'Packman'), with his auntie Amelia Heald. And then, he changes his name to Heald, sets up home with his cousin Eliza Jane and has two children! Couldn't find a marriage cert for them.
Yes, Jane Sergeant signed the death cert of her mother Mary in Shoreditch. And back to the will - no it doesn't say where 'middle' Philip was living. Philip One left his share of a sloop called the Abeona to his three sons Thomas, Philip and Roger, and there were other bequests (it went on a bit) to daughters Sarah and Mary, as well as another son, Richard. He leaves Mary (who seems to have an illegible surname ending in 'ing') an illegible sum of money. He leaves his daughter Sarah 'daughter of my said son Philip' the sum of £5. Looks like she was the only child he had at the time (can't remember if she was the eldest but she must have been). He doesn't mention her mother.
Incidentally, it may be worth noting that throughout this will all of the people mentioned who are involved in the sea trade, and most of whom own boats are referred to as 'Mariner'. So, perhaps the English records are less specific on this than they are in Scotland.
There are loads of Parkmans down on the Isle of Wight and on the Hampshire mainland as well. Some were smugglers and some worked for the customs and excise. The one I would love to find out more about was one Philip Parkman who stood trial for murder with two accomplices at the Winchester Lenten assizes in 1814. They were all working on customs boats and it seems they got into a fight with a French sailor one night at Lymington and he got stabbed. Parkman gave evidence against the other two. He and one of the others were both acquitted of manslaughter and the bloke who actually did the stabbing got two years. I suppose because the French were not flavour of the month in 1814, he got off a bit more lightly! But I haven't a clue which Parkman this was. I don't even know how old he was because I can't find any record that reveals this. Grr.
Finally, whilst wading through Lloyds this afternoon I took a little break and ran PP through Ancestry again. I found a burial of a Philip Parkman in a little village in Kent just half a mile from Ramsgate, in 1822. This is interesting, because Jane Parkman Serjeant consistently shows her birthplace in the census as 'Ramsgate'. Could this be the elusive Philip middle, I wonder? If he was about 50 when he died, then it might be. I'm trying to find out now whether there are any parish records still in existence for this church.