I would like to see a volcano poring out red hot lava, but I want to be safe. It seems like Iceland is a good place to see this. From a google there are many tours, that include pictures of people watching active volcano's, but we are having a disagreement about the scale, how close these people are to the active vent and flowing lava, is it tens or hundreds of meters from the vent.
How close can one safely get to such a scene of an active active vent and flowing lava?
The answer depends entirely on the volcano in question and the nature of the lava flow. If the question is how close is it possible to safely approach lava, the answer is for a docile and well behaved flow you can go right up to where you can touch the lava. I myself have done this a number of years ago at the Volcanoes National Park in Hawaii (get close enough to the lava flow that I could have touched it, I did not actually touch it). It was no more dangerous than standing near a campfire, albeit one that moved at a pace of a few inches per minute.
Let me just start by saying that by their nature, areas near erupting volcanos change rapidly, so you need very current information about any given situation. I have no idea what the situation is for the current eruption in Iceland.
That said, I was at Fagradalsfjall (which appears to be where your pictures are from) twice in May-June 2021, at two separate times a few weeks apart. The first time, the observation point was on a nearby hill, perhaps the same one as in your pictures. It was perhaps 100m away from the vent, which was more than close enough for me. It was close enough to feel the temperature change with each eruption. A couple people hiked a bit closer to near the flat flowing lava to the bottom right - I think the general opinion of everyone else there was that they were goddamn idiots. 
The hike up passed by some cooler flows that you could touch if you were so inclined - peeking in various holes under it would show glowing lava. Some hikers left hot dogs there to roast on the way up. 
When I came back a few weeks later, the path to the original viewpoint had been overrun with lava, so the new viewpoint was quite a lot farther back. However, one of the flatter valleys had active lava flows, moving quite slowly (perhaps a few cm/minute), so you could get as close as you wanted to. Within a meter or so tended to be too hot to stay for more than a few seconds. 
All of which is to say that depending on local geography and conditions, you can get as close as you feel comfortable to a lava flow.
I personally walked to less than half a meter (1-2 feet) next to red fast-flowing lava. It gets pretty darn hot, and your eyes start to hurt seriously from the heat radiation (imagine looking into a bonfire, but times 100), but otherwise the only risk is that the lava suddenly changes its flow over you. If that happens, you are dead; but the chances are small. Your call, of course, don't blame me if you die.
