The ending 십시오 adds the meaning of please in high formal situations. 걱정하지 마세요 is formal but not like 십시오. I believe 십시오 is used for people at very high ranks who deserve too much respect or for elderly people. My native korean teacher once told me that it's good to avoid using 십시오 to even your teachers or elders with whom you do not have much age gap. He told me that it's used for really old people like 할아버지, 할머니 or to people who require too much respect from you like your professor, etc. So, don't house it in your normal conversations with people. You can just use 세요 ending instead of 십시요 because the situations when you use 십시요 are a less colloquial. I hope it helps:)
괜찮습니다 means " I'm okay". It's Romanisation is "gwaen-chanh-seumnida". So you must be knowing that "ㅗ" has the sound of 'o'. That part of Romanisation is "go.." then it has "ㅐ" which looks similar to H. It has the sound "ae". So it makes it "goae". But it gets conjugated to give "gwae". (ㅗ+ㅐ = O+ae=wae). If u repeat "goae" many times and really fast you will realise that "oae" becomes "wae". So finally we get, "gwaen-chanh-seum-nida". I hope this explanation helps!!