Can I play games that recommends 2.4ghz?

I currently have a Windows XP, Lenovo, as a hand me down.
My system information is
Pentium (R) Dual Core
T4200 @ 2.00 GHz
1.99Ghz, 1.96GB of Ram.

I'm using a Laptop.

I have the following games on Steam: Goat Simulator, Team Fortress 2, Deponia, Garry's Mod, Viscera games. [some games can tend to be laggy at times; but when i lower the qualities; they're not really that laggy anymore. Is it my internet speed?]

I was wondering if these games were okay to play, since some of them recommend 2.2/2.4ghz; when i only have 2.00ghz. Will there be a problem even if there's just a few differences?
And if my laptop can't play these games, can you recommend me some gaming laptops/computers; Like the brand? I heard Dell was nice, but i'm not so sure about buying one. I'm not looking for very expensive ones, just average.
I know i asked alot of questions at once, but i just need an answer D;

Will if the games are for windows xp the games may be slow but you can play the games
go to www.hp.com windows xp is out o date on april 8 2014.

2.2 - 2.4 GHz are the recommended setting for the game to be playable on default settings at 30-60FPS +.
A dual core 2.1GHz pentium gave me 30+ fps on games like CSGO and World at War, that require higher up processors. Internet speed has nothing to do with this and only allows you to connect to multiplayer.
You should be fine with the 2GHz but definitely look at the RAM because some games will require 1-4GB RAM and you need about 512MB RAM for the OS and Windows Programs.
Hope this helps.
You will need to lower your settings.

The computer won't play many games so I recommend investing in a new computer.

I would recommend for a cheap budget:
Case: https://www.aria.co.uk/Products/Components/Cases/Midi+Tower/BitFenix+Comrade+Midi-Tower+-+Black+?productId=59627
HDD: https://www.aria.co.uk/Products/Storage/Hard+Drives/3.5+Inch+SATA+Drives/640GB+-+1TB/1TB+Seagate+Barracuda+Hard+Drive+3.5%22+SATA+III+-+ST1000DM003+?productId=48501
DVDRW: https://www.aria.co.uk/Products/Components/Optical+Drives/DVDRW+Dual+Layer+-+SATA/LiteOn+24x+Internal+SATA+DVD+RW+Drive+%5bIHAS124-14%5d+?productId=53312
CPU: https://www.aria.co.uk/SuperSpecials/Other+products/AMD+(Piledriver)+FX-6300+3.50GHz+(4.10GHz+Turbo)+Socket+AM3++6-Core+Processor+-+Retail+?productId=52724
MEMORY: https://www.aria.co.uk/Products/Components/RAM/DDR3/Dual+Channel+1600MHz/8GB+(2x4GB)+Crucial+Ballistix+Sport+1600MHz+CL9+DDR3+Dual+Channel+Kit+%5bBLS2CP4G3D1609DS1S00CEU%5d+?productId=54061
GFX: https://www.aria.co.uk/Products/Components/Graphics+Cards/AMD+Radeon/Radeon+R9+270/Sapphire+Radeon+R9+270X+Dual-X+Boost+OC+AMD+Graphics+Card+2GB+Graphics+Card+?productId=57842
MOBO: https://www.aria.co.uk/Products/Components/Motherboards/AMD+Socket/Socket+AM3++Piledriver+FX/Gigabyte+GA-970A-UD3P+AMD+Socket+AM3++Motherboard+?productId=57967
PSU: https://www.aria.co.uk/Products/Components/Power+Supplies/Non-Modular+650W+or+less/EVGA+500W+80+Plus+Power+Supply+(100-W1-0500-KR)+?productId=60504
Total Price Inc VAT £430-460
This can play pretty much every game and very high-resource demanding games such as battlefield 4 on max settings at 60-100 FPS. For £430, you really can't get much better.

Reason why I recommend?
I have the same graphics card and I can play every single game.

Hope this helps!
Also JackFrags has a youtube video on how to buy and build a cheap gaming PC!