All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is not permissible for a Muslim to use toys that include anything that contradicts the creed of Islam, or to help in spreading such toys as this is helping in spreading falsehood and distorting the creed of Muslim children; Allaah Says (what means): {Help you one another in virtue, righteousness and piety but do not help one another in sin and transgression. And fear Allaah. Verily, Allaah is Severe in punishment.} [Quran 5:2]
There is no doubt that the cross is one of the slogans of the non-Muslims and the people who have gone astray. Therefore, using toys that have crosses is promoting their beliefs and weakening the creed of amity and enmity for Allaah’s sake in the hearts of the Muslim children. This is indeed a very serious matter that is apparent to every person who has a sound mind.
Moreover, protecting the creed of the children from the causes of deviation is an obligation upon the guardians (parents); Allaah Says (what means): {O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones, over which are [appointed] angels, harsh and severe; they do not disobey Allaah in what He commands them but do what they are commanded.} [Quran 66:6]
Also, it is confirmed that Ibn 'Umar, may Allah be pleased with him, narrated that the Prophet said: “Every one of you is a guardian and is responsible for the people under his guardianship: the Imaam (Muslim ruler) is a guardian and is responsible for the people under his guardianship and a man is a guardian in his house and is responsible for the people under his guardianship…..” [Al-Bukhari and Muslim]
This is with respect to your first question.
As regards your second question, there is nothing wrong about the toys that include military vehicles, as such vehicles are used by both Muslim and non-Muslim soldiers and it is not expected that if the children use them, this will result in something prohibited. Also, the fact that they are made by non-Muslims is not Islamically an impediment that would prevent from using them.
Allaah Knows best.