Resent history > old times. It doesn't matter if Chrysler was killing it during the 90's, no one in their right mind should buy one of those today.

1. It's one of the bigger anime distributors in the North America. Not sure how much business they do worldwide. They're probably one of the best companies for english dubbed anime...not that there's a high bar or anything. Dubbed anime fans probably know them well...though this means nothing to me.

2. No idea

3. I don't believe the company has a presense in Japan itself, as they don't produce anime, merely distribute and localize it. 

4. Hopefully...no changes. I already have Funimation on my PS4, and it works fine, though I can't see myself paying more for it. Funimation and Crunchyroll currently share a lot of shows, which is good for me as a consumer, since I much prefer Crunchyroll's layout for watching anime. When I first subbed to the app, Funimation owned exclusivity on Assassination Classroom and My Hero Academia, though they seem to share these shows more often now. If this purchase does anything to affect this relationship, I'll consider it a bad move as a consumer.

5. Maybe...though I don't think this purchase really signifies that. Funimation isn't an animation studio, they just distribute and translate the content.

6. It seems they bought it for cheap, so it's likely a good purchase. No idea how successful the company is, nor do I really care much...I just hope they don't do anything to affect my enjoyment of the app as it currently is. When something isn't broken...don't try to fix it.

A-1 is an active anime studio with a good amount of popular recent productions. Aniplex licensed even more and more popular shows.

Is 2017 old times now?

Yup. Anything older than the Smiley movie doesn't  count. Also, personally, I have never really gotten into any anime Sony has been involved with since Kenshin. And they destroyed the second half of that anime by ignoring the manga.

Then you missed a lot of good animes.

Fairy Tail
Sword Art Online
Ao no Exorcist
Nanatsu no Taizai
Demi-chan wa Kataritai (<-- amazing)
Shigatsu wa Kimi no Uso
Boku dake ga inai Machi
Hei to Gensou no Grimgar
Oreimo
Working!
Saekano
Kannagi
Sora no Woto
Subete ga F ni Naru (<-- super amazing)
Servant X Service
Idolmaster
Sekai Seifuku
Qualidea Code
Galilei Donna

No shinsekai yori? :P

Then you missed a lot of good animes.

Fairy Tail
Sword Art Online