May one put tefillin on an uneducated Jew without first explaining to him the laws of keeping his body clean and conveying to him the seriousness of the sanctity of tefillin (is that even possible?)?
The Lubavitcher Rebbe zt"l addressed these and some related issues in a sicha (public address) of his on Shabbos Bereishis 5728/1967 (not long after he started the "Tefillin Campaign" in the weeks before the Six-Day War).
The relevant portions are printed in Likkutei Sichos, vol. 6, pp. 271ff (available on Hebrewbooks here and following pages). Your two points pretty well recapitulate questions #3 and #4 there (pp. 272 bottom, and following). Among the Rebbe's responses:
It is highly unlikely that when you ask a person who is not yet observant to put on tefillin, and he agrees to do so - that he will suddenly just then start having unclean thoughts (and presumably the same is true of bodily emissions).
The more so considering that it's a novel experience, and human nature is such that a person tends to focus their thoughts more at such a time.
Kavanah is of course important when performing any mitzvah, tefillin as much as any other, but it is not indispensable; the person still fulfills their basic obligation without it.
...and others which it would take me too long to excerpt. The following quotation from Chinuch (mitzvah 421), though, is noteworthy (some phrases of it are cited in the above sicha):
"...it is the opinion of our Sages, of blessed memory, that every person should hold fast to this mitzvah and do it regularly, because it is a great fundamental principle and a major protection against sin, and a strong ladder by which to ascend and enter into the service of the Creator, may He be blessed. Those who are strict about the holiness of this mitzvah and verbally dissuade the common people from being involved in it - perhaps they mean well, but in truth this prevents people from performing several [other] mitzvos, and it is a great harm... I know that 'there is no tzaddik on earth who [always] does good and never sins,' yet we should not prevent him from being involved in mitzvos when a good Divine spirit enclothes him do to good; for who knows whether he may continue in this good way until his death... As they, of blessed memory, taught us, 'one mitzvah brings another in its train...'"