Have a read of "Advanced marathoning" by pfitzinger & douglas as it has a section devoted to core strength etc.
I think it was from there that I had the advice to do it just after your lower intensity runs, as you are nicely warmed up and shouldn't be tired (i.e. don't do after a long run or an interval session). This should equate to two or three times a week.
that's a lot of questions! Here's my take on a few of them, but I'm sure there may be differing opinions.
Time vs distance: different philosophies for training and potentially depends on the target audience, as elite runners would cover bigger distance in the time period ( so a one hour run could be 10 miles for an elite, whilst it would only be 5 miles for a slower runner). Both systems work for some people - so its your choice which approach to take.
Sore back: It would be worth visiting a physio or sports therapist for a physical exam, but it is definitely worth adding some core strength into your marathon training.
bathroom: you said you were drinking water constantly - don't drink as much and see what happens. Do you take drinks during long runs? experiment with drinking at set intervals (e.g every 3 or 4m) during training. You should go into the race having a good idea of how often you will take a drink, and have practiced this in training. This is especially true at London its very easy to drink too much as there are water stops at every mile. NB You have to be sensible - if its a hot day then you take water from a few extra water stops - but you definitely don't want to take 26 drinks!
3x a week training: the more training you can do, then the better your result. If you want to make a significant improvement to your time, then you need to find time for more training. However, it is a balance between running and other commitments, and there are three day a week training plans, have a look at:
Standard warning - try them prior to the race to make sure they are OK for you.
I've used them throughout the summer after long runs and have felt a noticeable benefit. I haven't had the mild dehydration headaches that I used to suffer, and my thirst has been quenched whereas my old regime of a pint of squash would leave me thirsty about an hour later.
For my marathon next weekend, I'm planning before and after the race (same as DT19). I won't use them in the race as I only take a few gulps from a bottle from the water stops, so wouldn't take much in. You would also have to give the tablet a few mins to dissolve. Therefore for running races, they only make sense to me if you carry your own bottle.
Hi stingrayw2 and welcome, congratulations on completing your first run.
Have a look at couch to 5k programs to get you used to running. The biggest danger as a keen beginner is to try and do too much too soon, so this structures it with a combination of running and walking to get you started.
Key thing is to remember that recovery is just as important as running, as its when you are resting that your body adapts to the new demands you are putting on it.
Once you're comfortable with running 5k, you can then extend this to get up to 10k level.