On the history
To answer your last question there's no report saying that the Prophet () or the rashidun caliphs have imposed any custom on Muslims. Note that 'Omar has imposed some duty customs on non-Muslims with the approval of the sahaba.
But be aware that zakat is not the only income source of bayt al-Maal (or the treasury) بيت المال in an Islamic state which must be paid by Muslims themselves as there are the khums of al-Kharaj (one could say the income of mining but also from fishing activities etc.) and the khums of ar-Rikaz (a treasure that has been found on an estate) and the khums of al-Ghnana'im (war booty) and many more too. You may read in the book of the Maliki scholar at-Tawudi ibn Sudah التاودي ابن سودة "Kashf al-Hal" كشف الحال عن الوجوه
التي ينتظم منها بيت المال or take a look at this fatwa -in Arabic- on islamqa #138115. The first taxation on goods in Islam has been imposed around 310 aH.
Evidences and the position of Islam on custom duties (mukoos plural of maks)
Are taxes allowed or are they set equal to mukoos?
As for your first question the matter seems a bit unclear and we may find basically two different opinions: I clearly found fatwas allowing taxation for an Islamic state, while scholars such as al-'Izz ibn 'Abdassalam and al-Qurafi have clearly condemned imposing taxes on Muslims and set it equal to custom duties (mukoos) as it is taking money without the consent of the owner.
But when analysing these statements and reading them in the correct context a few things become clear:
The Islamic state is allowed to impose taxes in case that the treasury can't afford the necessities of the people such as hospitals, schools etc. in this case the state is allowed to ask for help or to impose taxes. According to scholars such as al-'Izz ibn 'Abdassalam, al-Ghazaly, imam al-Haramayn al-Juwayni and a-Shatibi in case that the treasury is empty or can't afford arming the Muslim army against an enemy the state can ask the rich people for money or even impose a tax, but they should check whether the soldiers and their leaders have some gold, silver or jewellery etc. too and they should only take as much as necessary. This is a fatwa or statement which allows taxation by incident only and not generally.
Ibn Taymiyyah as far as I could find held the opinion that taxation on Muslims is maks and haram (I wonder if he had the situation of an attacking enemy and an empty treasury in mind when giving this fatwa!). This is the view held by the Saudi Fatwa council too (See for example islamqa #42563.
So both opinions are basically held by scholars until today.
Basically all those who allowed taxation on Muslims by an Islamic state allowed it on the basis that the treasury can't afford the necessities of the population of the state such as education, security, health etc. and the imposed taxes shouldn't fill the treasury rather than fulfilling the needs of the population exactly without benefits.
One could also conclude that taxation is considered as injustice and theft if it has no justification in a necessity for the population and it is therefore to be taken as equal to custom duties (mokoos) unless there's a real necessity to impose them.
Some references -in Arabic-:
- Islamweb #592: The state is allowed to impose taxes.
- Islamweb #5811: Whether it is allowed to work as a tax collector.
- Islamway #10933: A Fatwa considering taxation as a necessity.
- Islamqa #25758: On the ruling of taxes on paid goods.