I use a Panasonic bridge camera too, not the same model but pretty similar, but I've had these problems with the autofocus and silhouettting against a light background, and have found ways to skirt round the issue! Probably totally 'wrong' and the only good advice would be to learn to use the camera settings properly, but for time-critical spur of the moment fixes just to grab a half-decent shot for IDing from, here's what I do!
The camera seems to set it's attention on roughly the same thing over and over again - once it's got the twig or leaf, it will keep refocusing on that repeatedly even if you're trying the button over and over again. To get it off the target it's chosen, I pick something else in the surroundings which is about the same distance from my camera as the thing I'm trying to get a picture of, and focus there instead. It can be a different plant further away or tilting down to the grass if my bird/flower/insect is close by but it keeps seeing past it, or aiming at a tree in the background if my target's a long way off and it keeps picking weeds in the foreground. Once the camera's focused onto the roughly-the-right-distance thing, swing back to your intended target, and press to focus again - nine times out of ten, it will latch on to the first thing it sees as it's adjusting it's focus, and if you've guessed your distance right, that should be your bird!
A similar technique works to get a quick and rubbish shot of a bird which is silhouetted against a light sky - having focused on the bird and realised the lighting is a problem, I pan away and focus on something a similar distance from me, but with a darker overall look - aim at the depths of the hedge rather than the twiggy tips with the finch balancing on, or into the shadowy side of the path rather toward than the bright reflecting water. This forces the camera to adjust for brightness, and it'll lighten your view on the screen dramatically - the second it does so, swing back to your bird and take one fast shot, quick as possible, without pausing to give the camera chance to refocus and adjust to give a darker picture. Your resulting photo will likely be terrible, but it will have identifiable features like colour and markings standing out, and occasionally you do get one which is good enough to keep rather than just ID from.
As I said, probably not the best of advice, much more knowledgeable forum members will likely be along with far better info if you want to learn how to work the camera properly, but as a couple of tricks picked up through trial and error over years of using a bridge camera badly, these do work!
