7.1 still has some small bugs/miss some basic features, you should create a trial & play around with it some time, before consider migrate or build new site
If the domain name remains the same, the content remains the same, the url structure remains the same, Google still perceives it as an old site, they will know that you just changed the template. I still often change the template and SEO is not lost.
But SEO will certainly be affected, good or bad, no one can be sure.
If my site already has good SEO rankings and stable traffic, I will strongly consider changing the template, because it can have a huge impact.