이다 + -서 is often spoken and occasionally written as 이라서 to be more clear. When you have noun + 이다 + -서 그런지 you can say ~이라서 그런지, so 명품이어서/명품이라서 and 시간이어서/시간이라서 are both acceptable. The last example is related in that the construction of 그런지 is based on verb + -ㄴ지 (in this case, 그렇다 + -ㄴ지) which is used to express that you are unsure. Instead of using 그렇다 + -ㄴ지, the final example uses 이다 + -ㄴ지 to mean "[might] be..." whereas 그런지 means something along the lines of "[if] it's like that..."

Frist and second sentences using 이어서/이라서 are equally same meaning and just different way of expression. Of course it conjugate whole lot of way depends on the context or what follows next but in all of those cases, they are either way to be used. Last paragraph, 예뻐서인지..meaning that you are guessing, not making a concrete statement by putting ...인지, They are looking at me maybe(perhaps) because i am pretty? kind of meaning.Over all, they are all same ways of expressing your opinion which is based on your guessing, or judgment. Not necessarily facts.