Auxiliary/modal verbs in Esperanto, are these correct?

[Uk_Polyglot]

I'm trying to figure out the main auxiliary/modal verbs in Esperanto for the present, past and future tenses, could you let me know if these are correct? Thanks...

To like - ameti
Present: 'I like' - Mi ametas
Past: 'I liked' - Mi ametis
Future: 'I will like' - Mi ametos

Would like - ametus
Present ('I would like') - Mi ametus
Past: 'I would have liked...' - Mi ????

To want - voli
Present: 'I want' - Mi volas
Past: 'I wanted' - Mi volis
Future: 'I will want' - Mi volos

To need - bezoni
Present: 'I need' - Mi bezonas
Past: 'I needed to...' - Mi bezonis
Future: 'I will need to' - Mi bezonos

To have to/must - devi
Present: 'I have to' - Mi devas
Past: 'I had to' - Mi devis
Future: 'I will have to' - Mi devos

To be able to/can - povi
Present: 'I can' - Mi povas
Past: 'I was able to' / 'I could' - Mi povis
Future: 'I will be able to' - Mi povos

Could (present tense), i.e. 'would be able to' - povus, 'I could' (present) - Mi povus

To have - havi
Present: 'I have' - Mi havas
Past: 'I had' - Mi havis
Future: 'Mi havos'

Was/were - estis

Also, is there a way to say 'should' in Esperanto? 'I should ea't, 'I should sleep', etc? What about the past tense of 'should', i.e. 'should have', 'I should've stayed', etc.

[Elishamod]

The word for 'should' is also 'devi'.
That is one of the few things I would like to change in Esperanto...

[Elishamod]

About the verbs, the forms are correct, but I'd use "ŝati" instead of "ameti".
Also, you did not use the complicated verb forms. i.e. "Mi estis manĝanta".
That helps with "I would have liked" - "Mi estus ŝatinta".

[Struthiomimus]

The word for 'should' is also 'devi'.

"Should" is expressed in Esperanto either by "devus" or by using the -u form of the verb. The nuance, as it was explained to me, is that:

Mi iru = I should go [and I will almost certainly go]
Mi devus iri = I should go [I *should* go, but in fact, I may or may not go]