Yes, there are live scores. I think the title is "general references" then you click that button you see in the same box as 10/4. Every match on Monday's OP is listed. It's a "by game" scoreboard so no points & you have to refresh (nightmarish memories from doing that during the Alex vs. Kiwi rnd of 16 last year. Yes, I still remember the score).
I believe that play is only happening on Centre Court where there's a roof. Alex is supposed to play last on Court 1 & the first match hasn't even started. Unfortunately, the weather is supposed to be worse tomorrow and only clear for 2 days.