Please tell me whether Muslims can socialize with Muslims who do not pray at all in Islamic functions and weddings where they have been invited. Furthermore can we drink and eat from the same cups and plates.

Praise be to Allaah.
Whoever does not pray at all is a kaafir and is not a Muslim, as is explained in the answer to question no. 5208.
Based on that, the woman mentioned in the question is not a Muslim, so it is obligatory to forsake her and not sit with her, unless that is for the purpose of encouraging her to repent and turn to Allaah by performing the prayers and doing so regularly.
It says in a fatwa issued by the Standing Committee for Academic Research and Issuing Fatwas:
“Whoever deliberately does not pray and denies that it is obligatory is a kaafir, according to scholarly consensus. If he does not pray because he is neglectful and lazy, then he is a kaafir according to the correct scholarly view. Based on that, it is not permissible to sit with those people, rather they should be shunned and ties broken off with them, after explaining to them that their not praying constitutes kufr, if you think that they are unaware of this ruling. It was narrated in a saheeh report that the Messenger of Allaah(peace and blessings of Allaah be upon him) said: “The covenant that differentiates between us and them is prayer; whoever neglects it is a kaafir.” This includes both the one who denies that it is obligatory and the one who does not do it because he is lazy. And Allaah is the Source of strength. May Allaah send blessings upon our Prophet Muhammad and his family.”
From Fataawa Islamiyyah, 1/373
With regard to eating and drinking from the same vessels that she uses, the ruling is the same as the ruling on the vessels of the kuffaar. It is permissible for the Muslim to use the vessels of the kuffaar if he knows that nothing haraam has been put in them, such as alcohol and pork. It was proven in al-Saheehayn (al-Bukhaari, 344; Muslim, 682) from the hadeeth of ‘Imraan ibn Husayn that the Prophet (peace and blessings of Allaah be upon him) and his companions used water from the haversack of a mushrik woman.
But if you are certain or you think it most likely that they have used them for any haraam things, then you have to wash them before using them, because it was proven in al-Saheehayn (al-Bukhaari, 5496; Muslim, 1930) from the hadeeth of Abu Tha’labah al-Khushani who said: I came to the Prophet(peace and blessings of Allaah be upon him) and said: “O Messenger of Allaah, we are in the land of the people of the Book, and we use their vessels for our food…” … The Prophet (peace and blessings of Allaah be upon him) replied: “With regard to what you mentioned about your being in the land of the people of the Book and using their vessels for your food, if you find vessels other than theirs, then do not use their vessels for your food, but if you cannot find anything else, wash them and then use them for your food.” This version was narrated by Muslim.
For more information see Fath al-Baari by Ibn Hajar: 1/453; al-Sharh al-Mumti’ by Ibn ‘Uthaymeen, 1/67-69.
And Allaah knows best.