Korean martial art similar to Karate ;literally art of hand and foot fighting

Then you need self defense training not karate. Karate is martial art art being the key word here, it's useful for self-defense but often is more of a hobby, way of keeping fit.
you don't want a jogging buddy to help you prepare for a marathon.
Most karate styles will be thought for months before you'll be allowed to fight, sparring will not provide you with real life situations that you may want to protect yourself in and you'll not be able to aim to cause harm, to another student wearing single layer of thick cotton.

The weapons that are used in Karate are: Bo Staff, Nunchako, Sai, Tonfa, and Kama. For more detailed information on these weapons, check out this website: http://www.livestrong.com/article/25014-type-weapons-used-karate/.

I have found a few sites that sell wall mounting displays for martials arts belts; however there are so many to choose from online - I recommend you do some extra searching of your own.

http://www.kochmartialarts.net/servlet/the-5783/karate-belt-display%2C-martial/Detail

http://www.kochmartialarts.net/servlet/the-7771/karate-belt-display%2C-martial/Detail

http://www.amazon.com/Personalized-Karate-Belt-Display-Rack/dp/B0069WOKYK/ref=sr_1_5?s=sporting-goods&ie=UTF8&qid=1346574646&sr=1-5

http://www.ebay.com/sch/i.html?_nkw=karate+belt+display

Many styles of martial arts use a belt ranking system; however they may not all equate to the same skill level. Here are a few styles and their ranking order:

Karate - white, yellow, orange, green, blue, brown and black

Tae Kwon Do - white, yellow, green, blue, red and black

Judo - only uses white, brown, red and black

Kung Fu - no established belt ranking system

The Kama is a traditional Filipino and Japanese farming implement similar to a small scythe used for reaping crops and also employed as a weapon. The Kama is often included in weapon training segments of karate and in some Chinese martial arts.

In Kobudo which is an Okinawin weapons style there is an excessive use in nunchakus . Altough not many actual Okinawin karate styles include the nunchucks. Many of the modern and sport karate's do, mainly for competition, and generally the way they are used is incorrect for fighting.

Karate belts are madefrom 100% cotton.

I found this site that includes a step by step tutorial video on how to tie your belt properly. http://www.all-karate.com/128/tie-karate-belt-photo-guide

By the integral parts of Karate. Do you mean Karate as martial arts or what?