1st of all Im not saying leading is a better srategy thank check calling. Some players prefere the 2nd.
Now. It depends on the villian , stack depth, board texture but its probobly better to be consistent with yuor strategy. You cant just lead with good hands and check the weak ones or the other way around cause its will be to ez to read for your opponent.
As a general rule vs unknown i see limped pots as free chips and they are there to be taken and in the early stage im gonna stab with any 2 cards and watch for my opponents reaction. Worst case scenario i get to fold my trash hands maybe bottom pairs or i take the chips there on the flop with trash or get to see next street cheaply and information about his range (information is always prizeless).
Not sure now but with the 6max structure u may not have that early stage game.
Once u get some information as mentioned before Its all about the villian , stack depth, board texture.
If I face a villain who raises most of his range or at least a decent % pre and Iimps occassionally I either raise preflop or continue stabbing any 2 especially on a dry board.
If I play someone who limps nearly all his range I will play as normal but will still lead with BP to see where I am regarding his range. Or x/r with BP if I expect a bet from him on the flop . Its all cheaper than x/c 3streets with 3rd , 4th or 5th pair facing a very difficult decision each time, cause u dont know where u are. I will play my draws aggressively as well, i tend to stab with a GS and xr with stronger draws.
On a dry board like in your posted hand a lot of times you are ahead with any pair on that flop. So why not take it there especially with BP when every card coming up next street is scary for you. As mentiond before worst case u fold hand that u were going to fold preflop anyway. Most times u gonna take the chips or see the next street cheaply and gain control. With shalower stacks in general ppl tend to tighten up a lot and fold more. Sometimes you may face someone who will automatically rr or shove over ur donk but they will pay u off when u hit strong or nuts.
You have to watch your opponent and see how is he reacting and then adjust accordingly. See how is he playing limped pots , if he is goin to bet him self or check behind (then u might get to showdown with some value and no action)? how is he gonna react to your donks? rr, xc , fold? on what boards?
Hope this makes sense and It wont confuse u. Im not the expert , only a $3.5 and $7 HU player climbing up the ladder and might be tottaly wrong
Would be nice to have some input from more expernieced players.
Anyways i personally prefere to lead or sometimes xr than xc in limped pots. Good luck.
As for the 2nd part of your question if you mean playing IP in limped pots for me its totally villain dependent. I dont tend to limp ever, unless im forced to. Ex. vs over agro opponent but this is a different subject and a long story and as i said I totally adjust my strategy to my opponent in that situation. I also have some limping range around 12bb deep but thats another topic i guess.