Of the five legendary fish, the Angler and the Mutated Carp are definitely the easiest to catch and with good practice won't require any special equipment other than an Iridium pole and basic bait.
The Glacierfish and Crimsonfish are much more difficult to catch due to how quickly they will jerk from the top to bottom of the scale. I have yet to catch the Legend; however, I was met with success in catching the other 4 by doing the following:
1) Craft premium bait (recipe obtained from Linus). The premium bait seemed to attract the legendary fish more frequently, which saves time spent attempting to catch them.
2) Purchase or craft a few Cork Bobbers and Trap Bobbers. The Cork Bobber (750g or 10 wood, 5 hardwood, 10 slime) expands the fishing bar. The Trap Bobber (500g or 1 copper bar, 10 sap) slows down how quickly the fish escape while not being reeled in. The bobbers will degrade, and having 2 of each will allow you to do a full day of fishing with no problem.
3) If your fishing level is not already 10, purchase or prepare skill boosting meals! The following meals will help you boost up your skill to 10, which expands your fishing bar as well.
Trout Soup : Fishing +1*
Chowder : Fishing +1
Escargot : Fishing +2
Fish Taco : Fishing +2
Dish O' The Sea : Fishing +3
Fish Stew : Fishing +3
Lobster Bisque : Fishing +3
*: Trout Soup is only 250G per meal from Willy's shop, so consider this an easy meal to bump from 9 to 10 if you're about to lose out on the season.
4) Keep trying and don't give up! If you're really tight on time, find a day with the perfect conditions (no crops to tend to or other responsibilities), and at the worst you can always 'Quit to Desktop' before the day is over to give it another day's attempts.
Other Advice:
For fish that like to jerk around in the water, always try to just barely have them caught. That way, when they dive up or down, you can react much more quickly and don't have to move as far.
DO NOT attempt to use the Barbed Hook on the Crimsonfish, Glacierfish, or Legend. You'll be spinning your wheels with how sporadically the fishing bar will 'adjust' -- (sway wildly).
Most definitely! If you have a relationship status with them, there will be a condition for you to have a cut-scene or mailbox interaction with them.
The following non-marriageable Villagers will each have significant involvement in a cut-scene you can experience:
Caroline, Clint, Demetrius, Emily, Evelyn, George, Gunther, Gus, Jas, Jodi, Kent, Lewis, Linus, Pam, Pierre*, Robin, Shane, Vincent, the Dwarf, Krobus, and the Wizard.
That leaves the following NPCs as without cut-scenes or only rewarding you with mailbox rewards for their relationship:
Gil, Marlon, Marnie, Morris, Willy, Mr. Qi, and Sandy.
Note that the cut-scene with Gunther will be unlocked once you donate enough Artifacts.
*: Pierre's cut-scene at 6 hearts is fantastic.
Best Answer
Stardew Valley has no official end to it. You can keep playing for as long as you like.
The closest thing the game has to an ending is getting a perfect evaluation by your grandfather. At the beginning of year 3, your grandfather's ghost will appear and score you based on a multitude of categories. If you get a perfect score, he will award you a statue that gives you free Iridium every day. If you've acquired this statue, it's safe to say you've 'beaten' the game, outside of any achievements or personal challenges you wish to work towards.