This is a matter of personal opinion - some will agree, others will disagree - but I don't believe that social media is a good way of making, reestablishing or maintaining friendships unless you also regularly see those people in real life.
Here's why I think that.
When Facebook was created it was for students on a college campus to sign up to. In other words, it was an additional form of communication for people that hung out in real life. Obviously, the scope has grown massively since then and it is not the only social network, but despite the constant efforts by the corporations behind them all to make us connect to more people so they can make more money, I believe that they work best when confined to the original scope which is why I have a personal "friending policy" for social media. I don't accept anyone onto my personal accounts unless I associate with them in real life.
I appreciate that your question is about people you don't see "often" - people that you did once spend time with in real life or occasionally still do - and so you might feel what I said doesn't apply. But consider one of the most common complaints that people have about social media. They say that people "misrepresent" their lives on there - showing you only the very best of their lives, from all the best angles. This I have found to be true, but it is not always an intentional deception. We only photograph or document the good times, and when you look at the social media of someone you spend time with you know that this is just the highlights because you are aware of the other not-so-good times. You may even have been around for some of those other times. If you connect to people you rarely see on social media then they may feel that irritation from looking at your "highlights" alone as they never see the rest of your life. They may see you as "dishonest", even if that is not your intention. And no, the answer isn't to put "bad times" on social media. If there is one thing more irritating than the Facebook friend who tries to make their life look more glamorous than it is it would have to be the friend who makes cries for help.
Really, the only kind of person I think you should include on social media that you do not spend time with regularly would be family. Our family want to see the best of our lives.
So I'm going to reframe your question - Are there any more effective ways to become closer friends with people I don't see often?
We all want real friends. A real friend will be happy for us to get their phone number. When you phone or text somebody it is personal - one to one. What you write or say is specifically for them and there can be no doubt that you are interested in them personally and not just saying something in public on social media to make it look like you have lots of friends. If I met a friend that I'd lost touch with I would ask them for their number and then text them, or message them on Whatsapp. I'd try and build up the friendship that way, through regular, personal contact. If they wanted to add me on social media that would be fine with me. Many SoMe apps find your friends from your telephone contacts anyway so one thing would lead to another, but I'd prefer it to be that way around because if I added someone on social media first and they accepted I'd wonder if it was just out of curiosity. It's too easy to connect that way. I'd then feel weird about using SoMe to ask for their phone number. If you are speaking about using Facebook to track down long-lost friends that you have no other way of contacting then I suppose you don't have a choice, but still, try to communicate directly first.
Having said all that, I believe that many people use Facebook messenger as their primary text-messaging service anyway. Also, at time of writing this, I'm aware that Facebook intends to allow cross-messaging between Whatsapp, Facebook Messenger and Instagram (all of which they own) and so some of what I have said might be redundant. Still, my point is that I firmly believe personal and direct communication is the only thing that really builds friendships. Posting things on a social media timeline is just like shouting into their air and hoping people hear. Most people don't warm to it unless you have an established friendship.
I feel this answers your supplementary question about people who don't often log into social media sites. If you ask for their phone number and communicate that way you don't need to worry about how often they log into Facebook. Also, if they quickly add you to their social media then you know they are regular users; if it takes them some time they may not use them regularly if at all.
Regarding interaction - replies to timeline posts - I think this also comes under my advice on establishing a personal rapport with someone ahead of anything else. Even with the best of intentions, you may irritate someone by commenting on their photos or comments. They may be putting things on there for their close family and friends with whom they share a history and possibly a sense of humour too. Comments from outsiders who may not appreciate either of those things may seem jarring. Your humour may not come across or you may misinterpret theirs. So again, don't make this your first way to interact with someone you don't know that well.
Additional: Just to clarify following your comment - I don't think there is anything unusual about asking for a phone number from someone with whom you have had some real-life connection, especially if you had a rapport. Just say something like "hey, we should keep in touch. Do you have a mobile number?".
There are millions of people out there who you could potentially have great friendships with but whom you may never chance upon meeting, but that is life. The best way to meet people is through people. Make an effort to be a good friend, even with people with whom you might not share lots in common. Every real friend that you make will introduce you to their friends. That is "real-life social networking" and is far more effective than staring into a screen.
