Fukua is arguably the best characters in the game. Her jumping HK is one of the best moves in the game, being a fairly noncommittal jump-in and combo tool. Her clone is generally a strong tool in neutral, and offers strong resets (especially MK clone), while her clone super is one of the best in the game, allowing her to continue comboing opponents after command grabs or some supers thanks to its recapture, crumple, AND teleport properties.
Another great tool for neutral is her fireball. LP prevents grounded approach, MP is for straight-up damage, and HP is an anti-air. LP is generally the best in long-range neutral, since it gives her time to use the MK clone. This allows Fukua to prevent most opponent's approaches, as they will get hit on the ground by the light fireball if they try to dash in, and most jump-in attempts will be blocked by medium clone, especially Instant Air Dashes (IAD).
As far as assists go, I'd go with the reccomended drill assist (medium I believe). It's a good pressure tool in block strings, and works as a combo tool as well. However, if you've got another assist that does similar, such as Double's Hornet Bomber or Big Band's Brass Knuckles, it might be better to use her medium clone instead.
Generally, I'd say Fukua is a character that can't be played in a "button-mash" style. Her tools are all unique, and she requires quite a bit of precision, such as with the aforementioned fireball-clone setup. If you are able to calm your nerves, control your inputs thoughtfully, and come up with a game plan, you can wreak havoc on your opponents; if not, you won't go nearly as far.
As far as team goes, I can do this in a later post. Generally, the more commonly-seen characters (parasoul, double, BB, Bella) go very well, but unorthodox characters (eg. Painwheel due to flight, Fortune) and characters that have very large flaws (eg. valentine and filia's reliance on assists, double's difficulty with zoning) tend to not work well with Fukua, since she's designed to be an all-around character.