Just to be clear, you need open-pollinated heirloom fruit to save seed from - you can't just go to the store and grow that apple or pear you purchase in the produce section. I suspect there may be suppliers out there somewhere that have such seed, but much more common is to purchase grafted stock, as the time from seed to fruit is many years.

Dan

Dan,
Thanks for your reply. I found a supplier on Ebay that sells fruit tree seeds. Not a huge fan of ebay but the sellers feedback is decent.

Pomegranates very iffy in your zone - they prefer a hotter climate to do well. And I'd second the suggestion to look for grafted seedlings (whips) rather than attempting from seed. Besdies the time involved to actually achieve a fruiting maturity, there is no guarantee that the seed you purchase is suitable to your location or will even produce a tasty, edible fruit....it might but it is just as likely not to. And despite what the feedback or reviews may say, I'd be extremely hesitant about purchasing from ebay. I know of too many instances when the item described (plants or seeds) is nothing like what is received or even a viable product. I know vendors selling what are known to be sterile seeds and purchases who do not know better are taken in. Buyer beware!

As to closeness, it makes no difference how close any of these various fruits are, as long as the trees have room to develop properly. You will also need the additional correct varieties for cross pollination of the apples, pears and cherries and that could be tough not knowing specifically what you are getting if purchasing from seed.

i have red dwarf and yellow delicious apples growing in zone 7 northern al. For an inexpensive source, check arbor day foundation. They do need a little room and a little time, but with a little luck and TLC, I expect some apples at some point.

pears (from same source) should be ok, but no direct experience here.

cherries have problems with the heat and humidity in the south, i have 3 varieties going (same source) well, but expect on the sour to one day pay off in terms of fruit

my strategy for the cherries, east side to burn off morning dew, shaded by house from about 3 pm on.

hazelnuts are also a good choice for limited space but they can get a blight in this part of the world

First, pears, apples and cherries are all different genera. As is the pomegranate. Thus they can be grown next to each other as they won't cross-pollinate, if that is the question.

Cherries need pollinators.

Second, I doubt you can put them out in a year and expect them to live, unless you cover for deer and maybe critters and wind, and baby for a couple years minimum. At least a decade for fruit if you are lucky.

Dan

Really. I understand trying to do things 'on the cheap' - believe me, I'm tight.
But you don't want to do seedling fruits of these species. Seedling apples/pears will eventually become very big trees, unless you're prepared to do constant, diligent pruning - fine if you've got unlimited space, but the typical residential yard can't really accomodate more than one standard apple, and you'll be waiting 10, 12, 20 years for them to grow through their juvenile period before you ever find out if the fruits they will produce are tasty enough to eat. You'll be far better off choosing grafted specimens of varieties you like on a rootstock suitable for your site. A grafted/budded selection will bear fruit in less than half the time you'd be waiting for your seedling to begin fruiting - and you'll know what the fruits will be like beforehand.
Pomegranates are easy to grow from seed, but typically, most seedling pomegranates do not produce top quality fruit. Better to purchase named-variety selections, propagated from cuttings. Most poms are zone 8(maybe 7) hardy - zone 6 is gonna be real iffy - but you might well succeed with some of the Russian selections, like Kazake and Salavatski.
Cherries - I dunno. Hard to beat a budded/grafted variety like Montmorency, though I've seen some seedlings of that one that were pretty close, in fruit quality, to the original.

Starting from seedlings....it would be several years before you could place outdoors on their own. Even with a ton of TLC, small seedlings and even trees just a couple years old would not be expected to survive if the area you are putting them is very active with people and animals.

Investing in quality grafted trees would be well worth the time and money.