Allow free growth but pay attention to clusters of shoots growing from a single point. They can quickly produce swelling and reverse taper. Thin out excess shoots as soon as you can decide which will be the leader and which might make good branch. Generally only 2 growing points from any place on a bonsai. A couple of extras can be left short term if you aren't sure but elms can produce lots from a single spot and need to be dealt with.
Small sized bonsai need to be managed more than larger sizes so you may find that vigorous shoots will need to be wired and/or trimmed before the end of the season. Usually the new apex will need more growth than branches as it needs to thicken more to match the old trunk and to help close the cut.
Be very wary of trying to wire very new shoots like the ones shown. New shoots are not strongly attached and will come off easily. Best to let these grow for a while until they change colour before attempting any changes in shape or angle.
Larger containers can boost growth rates. Sometimes bigger is not really better. Huge growth can quickly ruin the delicate balance needed for smaller bonsai. Growth needs to be managed to produce the desired results. Sometimes small plants do not respond well to really large containers. If roots are not able to colonise the whole space soil can sour? and growth is then reduced. Again, some balance and experience is needed.
Weeds can, and should, be managed. I don't think larger containers require much more water than smaller ones. Most water is lost through overspray missing the smaller container, water draining through the container and transpiration through the plants. Relatively little actually evaporates from the surface of a pot after the surface layer dries out and insulates the soil below.