‘(This) God forsaken country’ ---鸟不生蛋的地方（niǎo bù shēng dàn de dì fāng) or 被上帝遗忘的角落 （bèi shàng dì yí wàng de jiǎo luò）。Shouldn't be荒无人烟（ not so many population here ） Hit rock bottom----走头无路（zǒu tóu wú lù）situation reach the worse possible level 我要一个新的开始is better. Because 要is a single word here in predicate position, if like this, we usually try to avoid misunderstanding with other homophone word or avoid joining this single word with following single word into a new different meaning phrase. Therefore, either use measure word in between or use 需要to avoid the single word. somewhere I belong/fit in----属于我的地方. Depends on the situation you can use 归属，归宿。But these means final destination or means you will die there.

‘(This) God forsaken country’ —— （这个）鸟不拉屎(niǎo bù lā shǐ) /荒无人烟 (huāng wú rén yān）的国家。 'Hit rock bottom' —— 跌至谷底（diē zhì gǔ dǐ) '我要新的开始' or '我要新的开始' are both OK... 'somewhere I belong / fit in' —— 我的归属（wǒ de guī shǔ)/ 我的归宿(wǒ de guī sù)

"Oh wow major typo ..." Well, if you really care about the typo, then here is one typical example that you generally made in most of your previously posed questions -- "sentence", but not "sentance". (No flame please, as it is just a mutual learning and helping.) In my personal point of view, the other respondents have generally provided very good answers. For the third part of the question, i.e., "I need/want a new start", I would rather say it as「我 要/想 从新 (或：重新) 开始」. [N.B. If it is referred to a brand new start, 从新 would be better; if, however, it is referred to start something over again, 重新 would be the better term.] On the other hand, although「我要一个新的开始」looks grammatically fine, it somehow sounds strange when said in Chinese. Nevertheless, as a beginner in Chinese, I would say that it is not a main concern if you prefer this phrase. P.S. As a kind of personal suggestion, it would be a good practice if you may take your part by selecting the best answer of your posed questions (as you pose questions very frequently), so as to give a positive recognition to the respondents who have done their best to answer your questions.