For example, 나는 새롭게 태어났다 means 'I have been newly reborn, or I have been recently reborn, so simply I have become a different person'. 저는 가방을 살 거에요 and 저는 새롭게 가방을 살 거에요 have a same meaning. And just like I mentioned earlier, you can also say 가방을 저는 새롭게 살 거에요. or 새 가방을 살 거에요 저는 or whatsoever. Anyway, 저는 가방을 새로 살 거에요 means a bit different. It may imply that for whatever reason you want to buy a bag(can be new or used) again. 새롭게 사다 and 새롭게 가다 are different. They are not the same. The former one is 'to buy something again(could be in a same way or a different way)' The latter one is 'to go on(along) again(could be in a same way or a different way)'. If the geographical location of the origin of your mother language gets further and further away from Korea, you may find it harder to overcome such a lot of differences between the two languages. That's what linguists call 'Affinity' between two languages. English, for example, has NO affinity at all to Korean. If that is your case, hope you to take a significant effort to get used to Korean. It will be tough, really tough, but you can achieve it. Go for it.

1. As you understand, Adjective+게 works as adverb. That means you can put 새롭게 both behind and front of the noun. So 새롭게 주인공을 맡아서 = 주인공을 새롭게 맡아서 2. exactly 3. 새, 새로운 are Adjective. So it's position is always behind the noun. e.g. 그녀는 새로운 구두를 보았다. = 그녀는 새 구두를 보았다. but 새로, 새로이,새롭게 are adverb. So it's position is behind or front of the noun. which means 저는 가방을 새로 살 거에요 = 저는 새로 가방을 살 거에요 And 새롭게 is adverb. we use 새롭게 usually when describing something new(that didn't exist before) e.g. 그는 새롭게 컴퓨터를 개발했다. (He developed a computer that didn't exist before) so we usually don't use 새롭게 with 사다, 가다. Even I'm a native Korean, It can be wrong as I'm not an expert...Thank you for learning Korean. Have a nice day :)

One of amazing grammatical things in Korean is a flexibility in its order. For instance, let's say you want to say 'I have recently moved to an apartment' in Korean. As you can see the subject of the sentence is I(나는), the verb is have moved to(~로 옮겼다), the object is an apartment(아파트), and the adverb is recently(최근에). In English, it will make listeners a bit harder to understand if you say 'I to an apartment recently have moved', however, if that modification is made in Korean in a same way Koreans will understand without any problems. 나 아파트로 최근에 옮겼어. 나 최근에 옮겼어 아파트로. 아파트로 최근에 나 옮겼어. 옮겼어 나 아파트로 최근에. Whichever you say we understand. Specifically, in your question you asked about what if you change '새롭게 주인공을 맡아서' to '주인공을 새롭게 맡아서'. My answer is that there will be no difference at all. That's perfectly correct in Korean grammar. My answer to your second question is ABSOLUTELY correct. YOU ARE RIGHT!!! 새 is very likely an English adjective 'new'. So, if you say 나는 새 가방을 살 거에요, that means you want to buy a new bag. 새로 is likely an English adverb 'anew' and 'again' - You want to take a same action but in a different way or in a same way again. Therefore, 나는 가방을 새로 살 거에요 should mean that you will buy a bag again. But, that does not imply that you will buy a new bag. 새로이 is just like 새로 but its different sound make an expression richer. 새로운 is pretty much same as 새. It also has a different sound with 새, so provide speakers a variety of rhyming selection. 새롭게 is used in Korean in a way of 'newly' or 'recently' in English. It is not 100% matched with either of them, though, and sometime mix-used with 새로 or 새로이, however, the word is mostly used as newly or recently.