I am far from an expert but I will give it a shot.
Are they variants of 1903 Springfield?
no, the 1917 was based off of the pattern 14 enfield that was being built by remington and Eddystone on behalf of great brittain, when the united states was unable to build 1903 springfields fast enough to supply the troops remington, and eddystone along with winchester stepped forward with a modified pattern 14 design and called it the 1917.
How do I tell if it's the original barrel or not?
most still have the original barrels, it'll have the national ordnance acceptance stamp, makers initials and acceptance month and year stamped on the barrel just behind the front sight post.
If all the parts are matching?
most metal parts should have an E stamped on them to show eddystone, R for remington and if I recall correctly only select parts on winchesters.
What should I look for when looking to buy one?
you should make sure that the wood is in good condition with no signs of cracking, splitting or otherwise serious damage beyond cosmetic dings and dents. you should open the bolt and look down the bore to make sure it's not rusted out or shot out.
What are market value for them?
nowadays they average about $500 for original models, $350 for sporterized. exceptional condition models can go for north of $700 though
How do I tell if the receiver has problem or not?
unless it has been seriously abused there are no problems with the 1917 receivers.
Will the price for them appreciate when 2017(100 year anniversary of 1917) comes by?
short answer, no. these guns appreciate with supply and demand, there were millions of 1917s made but a number were sent to england for homefront security during WWII and others were sent to a number of resistance groups throughout europe and africa if I recall correctly. in addition the 1917, being such a robust design was popular with gunsmiths to convert to other calibers such as 300 win mag and many were converted into hunting rifles, some very nice ones, some hideous ones that were done with a hack saw and a drill. since the number of these guns in original, collectable condition are constantly going down and the number of people now wanting to collect are going up, they are constantly appreciating in value, so yes they will be worth more in 1917 but it will have nothing to do with the centennial.
Is there any s/n range that I have to be aware of?
short answer, no though very low numbers(under 100,000) are usually more sought after by serious collectors.
How does the action/handling compare to 1903?
completely different mechanics, the springfield is a cock on open design similar to many of today's modern sporting rifles while the 1917 is a cock on close mechanism that offers resistance on forward motion but aids in rapid extraction. it makes for a more fluid motion while cycling the bolt but is a little disconcerting for someone not expecting to have to apply forward pressure to chamber a round.
hope this helps