Against a smart fox, they aren't going to be giving you many free grabs if any at all. Against a good fox, you HAVE to master the 0-death. And if you are having trouble grabbing a fox, at low damages, all of DK's aerial moves lead into a grab. The easiest by far is the b air. If you manage to hit him with a b air, you can l cancel it and turn around for a free grab. (but you have to be quick). The way to beat a fox is grabbing and doing a 0-death. That is basically the only thing that DK has on fox (besides the Giant punch which is by far my favorite move in the game). DK can edgeguard fox pretty well also though. B air off the edge works well if you can get them (but don't go too low cuz DK's vertical recovery sucks butt). The best strategy is to grab the edge, and when fox is trying to do his fire fox, jump back and use your up b, knocking him back (as demonstrated by Captain Jack in Jungle Fever). If you knock a fox off the edge and you think he will use the illusion to sweetspot the edge, you can run towards the edge and use your up b (while still on the floor), and once you clear the ledge hold towards the center of the stage. The fox will run into you and get knocked down while it causes you to grab the edge, then from there, the fox has to make a vertical recovery. Ledge hop onto the stage with a d air. If the fox doesn't sweet spot it perfectly, he will be meteored down (but this can be cancelled). If he ledge techs or meteor cancels, you can try to d air him again, or do whatever you feel works best for you.
Falco is similar to fox with a few added things. Edgeguarding is easier against falco since his options are more limited cuz of his bad recovery (and the strategy against the illusion as mentioned b4 works on falco too. Don't worry, you won't get meteored from his illusion if you do it right.). The main difference here is trying not to get destroyed by the lasers and predicting the falco's moves. Falco's pillar combo is deadly if you don't know how to handle it. The biggest thing about beating a falco is you have to light shield against him. You won't be shield grabbing a falco much anyways so the light shield is definately the better choice in shields. When the falco comes with the d air, we all know that he will shine, followed by a jump, etc. If you light shield, you shouldn't be hit. After he does his d air and shines, he is gonna jump. You can use this to your advantage. If you jump when he does, you can do an u air. This catches falco users off guard all the time. Once you u air him, you can either go for another u air, or you can try and grab him. I do this all the time. If you grab him, you HAVE to 0-death him. The key to beating the space animals is not letting them survive if you get them in your hands. Also, another thing that can help, if after the shine, the falco shorthops, you can use an up b outta the shield. DK's up b outprioritizes falco's d air if timed correctly and has very good knockback if you hit them while they are above you.