The key q gives ⟨· ⁖ ⁘⟩ if pressed the right amount of times. Similarly, the key § can give ⟨◌̯ ◌̰ ◌̱⟩. The keys ì and ^ give ⟨ϳ⟩ and ⟨Ϳ⟩ respectively. The apostrophe ' can similarly yield the numerical symbols ⟨ʹ ͵⟩ when typed multiple times.
Diacritics are encoded as combining by default, rather that in precombined forms, because I think it eases the editing process (i.e. backspacing only removes one diacritic, and I often get them wrong). If you disagree, tick the checkbox. The copy button always normalises to NFC the text that is copied into the clipboard anyways. Typing a diacritic twice makes it full space instead of combining.
Type g= for ⟨ϝ⟩, ou= for ⟨ȣ⟩, st= for ⟨ϛ⟩, h= for ⟨ͱ⟩, b= for ⟨ϐ⟩ and p= for ⟨ϖ⟩, and their uppercase counterparts if present.
I recommend the font Gentium or Noto Sans for good coverage. If you have to deal with macrons and breves then I suggest SBL Greek. If you want this to work offline you can simply download the HTML.