For your first sentence, you are correct 'sir', as it is written and do not 'deviate' from their understanding and be 'deceived' by 'strange teachings', even from among us, different from what you have been 'taught' by the HOLY SPIRIT through the HOLY BIBLE.
Second sentence, yes 'is wrong' indeed and they are 'lies', both 'administrations' have been 'beguiled' by satan's 'twisted version' of the HOLY BIBLE and it is like, 'the blind leading the blind and soon they are going to fall into a ditch'. Sadly their 'plan of salvation' is 'partially' of 'truth', because that 'false salvation' will come from satan's 'messiah' to come, called the 'anti-CHRIST'. he will bring peace and be the liberator of all the problems to come upon this world, that henceforth after 'liberation', the people may do whatever pleases them, that which is 'right in their sight'.
Truthfully and faithfully 'abiding' Christian become 'a few' at that time of test/trial, as CHRIST said to HIS disciples and they will go through 'Tribulation' and 'Persecution' from the world under the 'influence' of the 'beast' worldwide. Many will 'abandon their faith' from the true MESSIAH of the HOLY BIBLE and have been 'beguiled' to believe in that 'false messiah', who will be so called, 'lovely' to the people around the world.
And moreover Apostle Paul said, 'that GOD will send a strong delusion on those who have not welcomed the Gospel' and faithful Christian must only say at that time of sufferings in helplessness and hopelessness that, 'FATHER forgive them, they knew not what they do'.
Have anyone 'welcomed' the four Gospel and everything written in them and 'abiding' according to them them?
Third sentence, yes and also not forgetting, muslim do 'abide' in HIM as 'Prophet Isa', but have not 'welcomed' the 'full' HIM, JESUS according to HIS 'Grace and Truth'.
'Abide in HIS word and love' means, one may take all the temptations/trials 'beatings' of their own 'flesh', the corrupt carnality/fleshly 'world' and 'satan' but never 'give in', still 'rooted to CHRIST's words/teachings', even 'lay down' their own lives for the love of their enemies.