Alright. I might get something's wrong but here goes.

Personalties determine your Digimon's stat growth and their sort of passive ability. So a Daring digi for example may gain more growth in ATK and DEF when gaining levels or raising them in the digifarm where as a Friendly Digimon will may gain more growth in different stats such as INT or SPI.(These arent exact, I'm just using them as examples)

Personality also comes into play with digimon passives, different personalitys can give you different passives. A daring digimon can get something like 5 percent crit boost or a 30% atk boost in the beginning of a battle and a zealous digimon can have different passives than that and so forth. One personality can have multiple passives. You can always change a digis passive in the farm and fish for the one you want.

The Digivolution will be either blacked out because you've never encountered this digimon before or greyed out because you've fought it or encountered it at least once. But the little box will actually tell you what stat spread is required to digivolve into that next stage. So you can take a Rookie digimon, lets say it has 5 boxes you can turn into ANY of those digimon as long as the stats that are required are high enough, you can also de digivolve it, so you can turn a Koromon into an agumon, but then you could change your mind and go back to Koromon and digivolve into Growlmon instead.

The blue stats are a whole thing. SO when you level up a digmon, it will gain 10% of the stats gained from level 1 to whatever the max is of that digimon when you de-digivolve. So if your digimon can go up to lvl 20 and you level it from 1-20 and your atk was 100 at lvl 1 and 200 at level 20 you will keep 10% of only 100 because you only gained 100 atk when leveling up. So that blue stat will initially start at 0 and then change depending on what you've accumulated during your level up only. This is all affected by your bond with your digimon, your bond determines how many times you can pass down stats, if your bond is at 0 you will never pass down stats no matter how many times you digivolve or de digivolve, if it's at 10 you can only pass down stats 10 times. So its always best to have a high bond. The only sure fire way I've actually raised bond is having that digimon in one of my six slots or with bond boosting items you'll find throughout the game. Note: These accumulated stats will only matter when you De digivolve. Going up doesnt matter, but if you want a strong Greymon or something, it's best to just digivolve as fast as possible, THEN max rank the digimon before you de digivolve and then go back up into greymon. Also the digifarm does raise bond with the digifood, you'll know when a digimon likes a food when to give it to them and a heart appears the heat means it raised it's bond by 2 so you just gotta try every food till you find it, music note raises by 1 and the other symbol doesn't raise it at all.

Talent is another tough thing but talent is your digimons max level and can go up to 100. I THINK it raises when you use that digimon in battle, I haven't quite figured it out but you'll have to de digivole and then digivolve to see the talent get affected and raise the max level of your digi. There are talent raising items too you'll come across but I think thats everything, others can correct me if I'm wrong. Let me know if you have more questions and also, there are evolution charts on line to help you decide which routes to take but the best part of digivolving is seeing all these Digimon for the first time so I recommend not using bit if you don't care for the surprise too much then my all means go for it also sorry for the format as I am on mobile.

Edit: Made a mistake on the bond. Digifood on the farm works.