Yes to all your questions.
Most of your answer lies outside. Firstly, and before you do anything else, reduce the level of the ground outside until it is 6" (150mm) below floor level inside, and make sure there is nothing growing in front of your airbricks (or that they're not obstructed in any other way). Also, check your gutters, downpipes, and other drains in the area. Downpipes need examining at their junction with the gutter, because a poor connection there can (and very often does) have the water from the roof running down the outside of the downpipe, and therefore not into the drain at all. Put a hose on your roof, and check that your downpipe is working properly. If it isn't, fix it. If your drains aren't working properly it is often just because they are blocked with rotten leaves and humus. If they are......sort them.
How many airbricks have you got, and how big are they? A photo or two will help.
Next, internally, dig all the soil away that you can which is built up against the inside of the outside wall. Ants, believe it or not, are a major cause of this problem (such soil is normally gorgeous, BTW......put it on your veggie patch!). Check your mortar with a pointing trowel? Is it soft and damp? If so, scrape as much out as you can, and repoint with whatever was used originally......be it lime mortar or cement. DON'T mix the two! Don't do this until we've decided on the airbrick situation, because you might be needing to knock another couple of bricks out to get some more air in under the floor.
Above all, don't worry. Your fixed-up floor will be separated from any damp, and most damp problems are easily sorted with the sort of access you have. And once you done all the necessary work, it might still take 6 months or a year for everything to get perfectly dry under there. No point looking in a few weeks and thinking that you've failed.