A Few Problems

I've been having a few problems with Minecraft lately, and I'm seeking some help.

On my laptop I get about 15-25 FPS when I look in a direction with few entities, but around 5-10 FPS when there are loads of them. Here are some specs:
Windows 10 Home (64-bit)
Processor: Intel(R) Core(TM) i5-3317U CPU @ 1.70GHz
RAM: 4.00 GB (3.88 GB usable)
Installed: Optifine and 2 other mods
I've tried using some custom JVM arguments but it doesn't really help, VBO's on or off (although one good thing with them, the "Loading Terrain" screen flashes by really quickly :D)
Video settings are also minimal, but they don't seem to help

Recently I'm unable to connect to servers on my computer. It gives a java.lang.NullPointerException: group error.
Specs:
Model: IdeaCentre-B320
Windows 10 Home (64-bit) - Java says it's 8(.1?)
Processor: Intel(R) Core(TM) i3-2100 CPU @ 3.10GHz
RAM: 8.00 GB
**Since the Pixel Format Not Accelerated error occurs due to the outdated driver which doesn't support Windows 10, I'm using Java 8u25 as a workaround. Servers had worked perfectly fine with this setting up till recently.
A sample of the Game Output log:

Spoiler: Game Output (Skaijie)

[20:12:16] [Client thread/INFO]: Connecting to astensity.com, 8121
[20:12:16] [Server Connector #1/ERROR]: Couldn't connect to server
java.lang.nullPointerException: group
at io.netty.bootstrap.AbstractBootstrap.group(AbstractBootstrap.java:80) ~[AbstractBootstrap.class:4.0.23.Final]
at net.minecraft.network.NetworkManager.func_181124_a(NetworkManager.java:330) ~[eo.class:?]
at net.minecraft.client.multiplayer.GuiConnecting$1.run(GuiConnecting.java:68) [bfa$1.class:?]
I may have typed part of it wrong because the problem is on the computer and I'm creating this thread on my laptop XD

Full log here
Hamachi is installed on the computer. I've tried turning it off but it doesn't work.
Error also occurs on vanilla Minecraft and other versions (e.g. 1.8.9)

So, how do I fix it?

 

You using cracked Minecraft or what? It looks like the client is having difficulty connecting outside, disable your firewall?
For your laptop, you either need to clear some things off your hard drive or Your graphics chip just sucks

I also have no knowledge of java so I'm just trying to make sense of the log

 

Dude, if you get the chance to buy another computer, buy a MacBook Pro. I can get over 100fps easily with optifine. For now, it seems as if your computer is the problem. I used to play with a computer which crashed every time I lit a block of TNT

 

Every person who games on the internet would disagree with you on that
Just get a computer that has decent specs and wasn't created before 2012, it should run minecraft at stable performance

 

^^

i've tried copying my laptop copy of cracked minecraft over to the com, it doesn't work, so probably a firewall or something.

 

Oh... so that's why
Copying minecraft over to another Xin won't just work. You can copy the saves, resource packs and a few other files over but copying the entire minecraft folder to another comp and expecting it to work wont happen,
You have to re install minecraft. BUT of course backup accessible data like your worlds, resource packs and servers first