For the fill button, disassemble and clean. This is the same place I started when I first got my machine. I will say that it was the pebble that started the avalanche; I ended up disassembling the entire machine. This much work may not be necessary for either of you, but I never regretted it.
For the flexible hose, there are two options. One is find the same diameter hose at the hardware store - something that feeds water to your kitchen tap. Carefully cut the collar from you old fittings so you can press the fitting into your new hose. Use a hose clamp to fasten. Total cost about $10.
The second way is to take the hose to a local hose fabricator and they will make you something out of all new parts. Not sure what the cost would be.
They machines are great and worth the effort!