Hi @Anonymous
It is all possible and relatively straight forward in PowerApps too. You just need to change the way you think.
To hide a control, you just use the control's Visible property, and it can be set to a formula that depends on other dynamic values.
To show a message, you place a label and use the label's Text property or Visible property to show when appropriate.
To switch between pages you use the Navigate action
To query for data you use the shaping functions (Filter, Search etc.)
To submit data you use the Patch function, to send an email you add Office365 connection and then the send email function appears
To close the form you use the Exit function
To not run 'rules' you just put the logic in the control properties.
It's all in the documentation, although sometimes not very well explained.
PS I always start to build my forms from the single controls instead of using the out-of-the-box forms available. In the end this is much easier if you require any customisation. In other words I start with a blank app instead of creating the app from data, and I don't use the form controls.