These two verses in Sura Al-Baqara are very clear that no friend can intercede to his friend on the day of Judgment just because of their friendship or partnership (O you who believe, Spend from what have provided you, before a Day comes when there will be no bargaining, nor friendship nor intercession). This is stated in verse 2:254. It is clear that mere friendship or partnership will never allow intercession. In verse 2:255 which is known as Ayatul Kursi, it is stating that no one can intercede but only by Allah's permission. There is no contradiction at all if you understand the real translation of the verses.
Verse 2:254 refutes materialistic intercession, while verse 2:255 states the real intercession by permission of Allah.
The meanings of the Quranic verses can not be taken just from the superficial linguistic meanings. Allah (SWT) Has clearly mentioned in Quran that it is the responsibility of the Prophet (SAWA) to explain to the people the real meanings of Quran (Sura 16, Verse 44).
The meaning of Sura Al-Hamd verses which you quoted never suggest not to seek Waseela. Prophets were mentioned in Quran seeking help from people like Prophet Musa (AS) who asked people for food, and Prophet Sulaiman (AS) who asked people to help him in getting the throne of Bilqees.
We believe that no one can help with out the permission of Allah (SWT).
We do Tawassul because we are been ordered by Allah (SWT) to seek Waseela ( Sura 4, Verse 64.