1. It depends on the shape, rectangle, square or round ponds are easier to calculate rather than odd shaped ponds- if the pond has levels (like a lot of ponds do), split the pond up into sections when calculating the gallons and then add the total up.
There are numerous pond calculators available on the internet, although its best to try at least a couple and see what results they turn up and then decide on the most likely result (as some can vary a bit).
If you have a water meter, you can use that to accurately judge the amount of gallons, or you can work out how much water comes out of the hose per minute and then calculate how much water is in the pond based on the length of time it takes to fill up etc.
A 1000gal pond with 4ft depth is the advised minimum for koi, while any pond 300gals or more is fine for goldfish as long as it has at least 3ft depth. If you live in a particually cold climate (where water regually freezes in winter), and have some cash to spare, you may want to consider heating (which has numerous bennefets for fish, particually koi).
Good filtration is very nesarsary for the health of the fish, as well as allowing you to stock the pond more (as non-filtered ponds are only supposed to have very small quantities of fish).
2. To find the right length liner, you should measure the length of the pond twice the maximum depth, and to find the right width liner, calculate the width of the pond twice the maximum depth- you may want to add a little extra liner on top of these calculations to be on the safe side as well.
This is how we did it at least for out pond, and we had a fine amount of liner to go around.
Before you put in the liner though, you should put sand on the sides and bottom of the pond (to prevent rocks or roots from puncturing the liner over time) and underlay as well, which will help insulate the pond and cushion the liner.
Depending on your soil type, if the soil is thick with clay you probably won't have any problems digging a secure pond, however soil like dry chalky soil can not hold up very well so you may want to brick the sides of the pond securely into place or support them some other way to prevent them from caving in.
3. Plants are mostly judged by the depth at which they grow best at i.e. some grow right at the bottom (like lillies, which often need 3ft or more depth to grow properly), while others grow at mid level, others in shallow waters, while others only grow well when partly submerged. There are also bog plants, which are not really true pond plants at all, but rather grow best in waterlogged soils.
Always check how large (tall, deep or wide) the plant grows (and how fast) as some pond plants can easily choke ponds if the ponds are not very large.
Also decide on wether you mind having plants which only come out in the summer, or ones which stay green and healthy throughout the whole year.
A lot of pond plants need to be cut back during winter, or bennefet from occasional pruning to incourage fresh growth as well.
You will also probably want to get bigger containers for any plants you buy, as many plants sold at garden centres come in containers far too small for them to grow healthily in the long term.
Pond plants in general are designed to thrive off very little nutrients, and will be fine in a plastic basket-like large container with gravel or pebbles and only a small sprinkling of soil mixed in. If the pot has too much soil in it, it can give the pond really bad algae problems due to all the excess nutrients.
4. I don't know much on koi, but for feeding goldfish and koi in general a varied diet is best (one that contains both veg and high protein foods).
Do not feed the fish if the temp in the pond falls below 10 degree's as this is too cold for most fish to digest food properly- feeding fish when the temp is too cold can result in bad constipation or other digestive system related disorders.
