Installed the mod on the Server. My game runs smoothly, but the server isn't. When i break a block it reappears and one second later it drops as an item and disappears again. Opening chest and stuff works normal most of the time, without delay, didn't try to open a chest next to the Portals, maybe that was an issue. But flying anywhere on the Server with a Paraglider lags too, as soon as i right click it should open --> 3-5 seconds delay though. Server is running good, not too much cpu or ram used, seems these lags only affect some things in the world (Items [Food, potion drinking --> eating for ages, food just not dissapearing ], block breaking) chests are not really affected by the lag.

Another thing is portal linking. The mod spawned a new Portal at the exact coordinates in the Nether, including Y. my other portal was 5 blocks away horizontally and about 30 blocks vertically.
But that's not that bad :P

Chests should be no different than any of the other things you've listed. How about other server-side inventories (e.g. horses)?
Are there active portals on the server? Is it any different without them?
If it's neither CPU nor RAM that's limiting, it's likely the network. Is the server's network fine? Is your network fine? Do other people have the same issue? Do you have the issue in singleplayer?
What other mods are you using?
Please post the full server log. That'll also answer the mods question.

Another thing is portal linking. The mod spawned a new Portal at the exact coordinates in the Nether, including Y. my other portal was 5 blocks away horizontally and about 30 blocks vertically.

Unless your "other portal" was an empty obsidian frame of exactly the right size and shape, this is expected behaviour. Unlike vanilla, there's no way to have two portals linking to the same destination, so it always creates a new one unless it can find an empty obsidian frame.
Also, I think I've mentioned this before, but keep one issue to one topic!

Used a backpack and my own Inventory, they were lagging/ i put blocks in my hotbar, swapped back to their old places. couldn't test horse inventories, survival server, i'm no admin, backpack might be kind of the same?
Yes, active portals were two on the Server, one about 100 blocks away, and one i tested with. In singleplayer it works just fine without lag. And yes, everybody on the server had the issue, as soon as they got about 50-70 blocks in portal range. But as soon as i destroyed the portals it worked fine.
Better portals and forgelin have been took out, works all fine now, serverlog comes as soon as i get it. ( not my server )

latest.log

Hmm, there's no trace of Better Portals in that log, so it's only of very limited use. Could you get the log from when BP was installed and when the lags were happening?

Does that modpack happen to be publicly available on CurseForge so I could try myself? Is it obvious and I'll immediately notice or does it only happen occasionally?

And yes, everybody on the server had the issue, as soon as they got about 50-70 blocks in portal range.

Are you saying that anyone who got in range had the issue while those outside did not (as opposed to everyone had the issue when anyone is in range), i.e. can people in range be affect and at the same time those outside be unaffected?