Is there any problem praying in the same way as Muslims from other sects? And if I was praying alone?
We are not to pray how other sect pray if it is different from how the Prophet prayed, just like we are not to pray how other religions pray (I think that one is quite obvious), the rule is to Pray as the Prophet ﷺ prayed, as he ﷺ said:
صَلُّوا كَمَا رَأَيْتُمُونِي أُصَلِّي
Pray as you have seen me praying
So we are not free to choose whichever way we want to pray, one should try hard to pray the correct way.
This answer is primarily from a sunni point of view:
Sunni Muslims are the largest denomination of Islam also known as Ahl as-Sunnah wa’l-Jamā‘h. The word Sunni comes from the word sunnah, which means the teachings and actions or examples of the Islam's final Prophet Muhammad (SAW). Therefore, "Sunni" refers to those who follow or maintain the sunnah of Muhammad. In many countries, overwhelming majorities of Muslims are Sunnis, so that they simply refer to themselves as "Muslims" and do not use the Sunni label.
In terms of fiqh, the major schools of thought (madhhab) are:
It is named after the scholar Abū Ḥanīfa an-Nu‘man ibn Thābit (RA) (d. 767), a tabi‘i whose legal views were preserved primarily by his two most important disciples, Abu Yusuf and Muhammad al-Shaybani.
As the fourth Caliph, Ali (RA) had transferred the Islamic capital to Kufa, and many of the first generation of Muslims had settled there, the Hanafi school of law based many of its rulings on the earliest Islamic traditions as transmitted by Sahaba residing in Iraq. Thus, the Hanafi school came to be known as the Kufan or Iraqi school in earlier times.
In the early history of Islam, Hanafi doctrine was not fully compiled. The fiqh was fully compiled and documented in the 11th century.
It was founded by Malik ibn Anas (RA) in the 8th century. The Maliki school of jurisprudence relies on the Quran and hadiths as primary sources. Unlike other Islamic fiqhs, Maliki fiqh also considers the consensus of the people of Medina to be a valid source of Islamic law.
Maliki school's sources for Sharia are hierarchically prioritized as follows: Quran and then Sahih Hadiths; if these sources were ambiguous on an issue, then `Amal (customs and practices of the people of Medina), followed by consensus of the Sahabah (the companions of Muhammad), then individual's opinion from the Sahabah, Qiyas (analogy), Istislah (interest and welfare of Islam and Muslims), and finally Urf (custom of people throughout the Muslim world if it did not contradict the hierarchically higher sources of Sharia).
The Maliki school differs from the other Sunni schools of law most notably in the sources it uses for derivation of rulings. Like all Sunni schools of Sharia, the Maliki school uses the Qur'an as primary source, followed by the sayings, customs/traditions and practices of Muhammad, transmitted as hadiths. In the Mālikī school, said tradition includes not only what was recorded in hadiths, but also the legal rulings of the four rightly guided caliphs.
It was founded by Imam Al-Shafi`i, a student of Imam Malik, in the early 9th century.
The Shafi school predominantly relies on the Quran and the Hadiths for Sharia. Where passages of Quran and Hadiths are ambiguous, the school first seeks religious law guidance from Ijma – the consensus of Sahabah (Muhammad's companions). If there was no consensus, the Shafi`i school relies on individual opinion (Ijtihad) of the companions of Muhammad, followed by analogy.
The Shafi`i school of thought stipulates authority to five sources of jurisprudence. In hierarchical order, the school relies upon the following sources for Islamic law: the Quran, the Sahih Hadiths, the ijmā' (consensus of Sahabah, the community of Muhammad's companions), the individual opinions of Sahaba with preference to one closest to the issue as Ijtihad, and finally qiyas (analogy).
The Shafi`i school rejects two sources of Sharia that are accepted in other major schools of Islam - Istihsan (juristic preference, promoting the interest of Islam) and Istislah (public interest)
It is named after the Iraqi scholar Ahmad ibn Hanbal (RA) (d. 855), and was institutionalized by his students. Imam Hanbal was a student of Imam Shafi`i.
Hanbali school derives Sharia predominantly from the Quran, the Sahih Hadiths, and the views of Sahabah. In cases where there is no clear answer in sacred texts of Islam, the Hanbali school does not accept jurist discretion or customs of a community as a sound basis to derive Islamic law, a method that Hanafi and Maliki Sunni fiqhs accept. Hanbali school is the strict traditionalist school of jurisprudence in Sunni Islam.
The reason I gave a brief background is to highlight the fact that all the Imams used the Quran and Sahih Hadiths as their primary source. It is only when an issue arised on which both were silent did they opt for other methods.
None of the Imams would have ever said that their word is the final word and not to follow any other Imams. Infact there is a famous statement where one of the Imam even says to throw his fatwa on the wall if later it is found to be going against the teachings of the Prophet Muhammed (SAW).
Inshallah all the Imams are on the straight path and all of them have thought the ways of the Prophet. It is only the later generations that have made these differences and spread the notion of following only one Imam.