Hi, welcome to the forum!
Pumps come with clips, so that you can clip it onto your clothing (ie waistband of trousers, bra - if you're female!). It also obviously goes into any pockets you have!
It depends what sort of dress - anything body-hugging and tight all over and you'll probably be able to see wherever it's clipped to, but anything else should have somewhere to hide it! You can buy belts that sit flat against your stomach to carry it in, there are also straps to go around your leg to hold it. Plenty of places!
Yes, the tubing is attached to the pump - that's how it delivers insulin to you. There is a new, tubeless pump that has only just reached the UK market - the OmniPod - but this means the pump itself is attached to your skin and a lot harder to hide.