Need help with verbs

Hello everyone! Happy new year.
I have began to learn Japanese 2 weeks ago. I have chosen to start Rosetta Stone just to get familiar with the language. I have a question about the verbs "Desu" and "Arimasu". I understand that the verb "Desu" means "to be", covering "i/is/are". I am not clear as to what the verb "Arimasu" means although it seems to be similar to "Desu". For example:
(Excuse me, for I do not have the tools to write in hiragana. Ill try my best in romanji.)
Tamago ga itsu arimasu
I assume this sentence means "There is an egg/There is one egg" but why wouldn't it just say "Tamago ga itsu desu". Like i said I am pretty new to this so excuse me if i am wrong. Also, i have just finished learning all my hiragana, could someone perhaps refer a website to learn katakana? In addition, I have read through the forums and i have noticed what i believe are Chinese characters. I have read that the Japanese borrowed Chinese characters in order to make the current syllabary, and they seem quite essential to understand. Could someone refer me to a place i can learn the meaning of these characters (I believe is kanji)? Again, my apologies for all these questions. Thank you for anyone taking the time to read this and help.

De''ru''(Demasu, Dekakemasu...etc) can have many meanings. Desu refers to is/are is not a verb.
Arimasu means to exist.
Desu (in your case) don't have much meaning for a whole sentence since sometime desu can be omitted, arimasu only use with non-living things and sometime can be omitted as well.
Those 2 can't be described in English. They are just there to sound more convenient I think.
In your example, it should be ''hitotsu'' instead of itsu.
If you want to use desu in this case, particle wa is used instead of ga and it should be:
Tamago wa hitotsu desu.
Hope it helps.

"Desu" is a copula. Wikipedia has a brief explanation of it.

Copula (linguistics) - Wikipedia, the free encyclopedia

"Tamago ga hitotsu arimasu" is a "stand-alone" description, whereas "Tamago ga hitotsu desu" can be used only in a context, for instance, as an answer to the question "What and how many items are in the box?" or like that.