Those quotes are very often used by non-Muslims and yes they are very much out of context and very misunderstood.
The explanations and true meanings are going to be lengthy. I will begin with just the first one.
"Seek out your enemies relentlessly." (Surah 4:104)
First of all not only is that out of context, it is just part of the ayyat it was taken from and not even a very good translation.
Let us look at in more context.
4:96. Ranks specially bestowed by Him, and Forgiveness and Mercy. For Allah is Oft-forgiving, Most Merciful. S P
4:97. When angels take the souls of those who die in sin against their souls, they say: "In what (plight) Were ye?" They reply: "Weak and oppressed Were we in the earth." They say: "Was not the earth of Allah spacious enough for you to move yourselves away (From evil)?" Such men will find their abode in Hell,- What an evil refuge! - S P C
4:98. Except those who are (really) weak and oppressed - men, women, and children - who have no means in their power, nor (a guide-post) to their way. S P C
4:99. For these, there is hope that Allah will forgive: For Allah doth blot out (sins) and forgive again and again. S P
4:100. He who forsakes his home in the cause of Allah, finds in the earth Many a refuge, wide and spacious: Should he die as a refugee from home for Allah and His Messenger, His reward becomes due and sure with Allah: And Allah is Oft-forgiving, Most Merciful. S P
4:101. When ye travel through the earth, there is no blame on you if ye shorten your prayers, for fear the Unbelievers May attack you: For the Unbelievers are unto you open enemies. S P C
4:102. When thou (O Messenger) art with them, and standest to lead them in prayer, Let one party of them stand up (in prayer) with thee, Taking their arms with them: When they finish their prostrations, let them Take their position in the rear. And let the other party come up which hath not yet prayed - and let them pray with thee, Taking all precaution, and bearing arms: the Unbelievers wish, if ye were negligent of your arms and your baggage, to assault you in a single rush. But there is no blame on you if ye put away your arms because of the inconvenience of rain or because ye are ill; but take (every) precaution for yourselves. For the Unbelievers Allah hath prepared a humiliating punishment. S P C
4:103. When ye pass (Congregational) prayers, celebrate Allah's praises, standing, sitting down, or lying down on your sides; but when ye are free from danger, set up Regular Prayers: For such prayers are enjoined on believers at stated times. S P C
4:104. And slacken not in following up the enemy: If ye are suffering hardships, they are suffering similar hardships; but ye have Hope from Allah, while they have none. And Allah is full of knowledge and wisdom. S P C
4:105. We have sent down to thee the Book in truth, that thou mightest judge between men, as guided by Allah: so be not (used) as an advocate by those who betray their trust; S P C
4:106. But seek the forgiveness of Allah; for Allah is Oft-forgiving, Most Merciful. S P
4:107. Contend not on behalf of such as betray their own souls; for Allah loveth not one given to perfidy and crime: S P C
4:108. They may hide (Their crimes) from men, but they cannot hide (Them) from Allah, seeing that He is in their midst when they plot by night, in words that He cannot approve: And Allah Doth compass round all that they do. S P C
4:109. Ah! These are the sort of men on whose behalf ye may contend in this world; but who will contend with Allah on their behalf on the Day of Judgment, or who will carry their affairs through? S P
4:110. If any one does evil or wrongs his own soul but afterwards seeks Allah's forgiveness, he will find Allah Oft-forgiving, Most Merciful. S P
4:111. And if any one earns sin. he earns it against His own soul: for Allah is full of knowledge and wisdom. S P C
Yusuf Ali's Quran Translation
Although to understand it much better you would need to know the entire Surah it is taken from and as to what is being spoken about. But, I believe that this is sufficient to show that it is reference to enimies that have attacked Muslims and this is part of the guidlines for self protection.
Astagfirullah