1) How likely is intracranial thrombophlebitis after nasal hair removal?
Cavernous sinus thrombosis (Stat Pearls, 2019) after nasal hair removal (or from any cause) seems to be rare but possible:
...annual incidence of cavernous sinus thrombosis might be
approximately 0.2 to 1.6 per 100,000 per year.
Cavernous sinus thrombosis (CST) is a rare, life-threatening disorder
that can complicate facial infection, sinusitis, orbital cellulitis,
pharyngitis, or otitis or following traumatic injury or surgery,
especially in the setting of a thrombophilic disorder. Early
recognition of cavernous sinus thrombosis which, often presents with
fever, headache, eye findings such as periorbital swelling, and
ophthalmoplegia, is critical for good outcome. Despite modern
treatment with antibiotics and anticoagulation, the risk of long-term
sequelae, such as vision, diplopia, and stroke, remains significant.
Antimicrobial therapy includes an anti-staphylococcal agent
(vancomycin if methicillin resistance is high, or nafcillin), a
third-generation cephalosporin, and metronidazole (for anaerobic
coverage) as well as antifungal therapy with amphotericin B. A
prolonged duration of parenteral therapy, typically three to four
weeks or at least two weeks beyond clinical resolution is suggested.
As many as 50% of survivors might have sequelae, most commonly third
or sixth nerve palsy. Other complications can include sepsis,
meningitis, subdural empyema, brain abscess, blindness,
panhypopituitarism, intracranial hypertension, infectious arteritis or
mycotic aneurysm of internal carotid artery, vasospasm, septic emboli,
stroke from carotid narrowing, cortical vein thrombosis or hemorrhagic
infarction, coma, and death. Mortality rates as high as 80% in the era
before antibiotics have diminished to below 8% to 13%.
The Dangerous Triangle (Still Dangerous) (JAMA, 1969):
Report of a Case:— A 31-year-old woman was first seen by a physician
Jan 13, 1966, with the report that she had plucked some nasal
hairs two days before. This was followed by edema and soreness
around the dorsum of the nose. The patient received penicillin
intramuscularly and was instructed to place hot packs on the nose.
Twenty four hours later, the penicillin therapy was repeated, followed
by an antiinflammatory dose of radiation to the nose.On Jan 16, marked
edema and discoloration of both eyelids and periorbital areas...
Plucking hair could spread the infection from the pre-existing infection in the nasal mucosa, for example, due to a pimple or boil or bacterial sinusitis or from contaminated tweezers, especially when plucking is associated with bleeding.
Cavernous sinus thrombosis caused by contralateral sphenoid sinusitis: a case report (Head & Face Medicine, 2013):
...more recent reports suggest that sinusitis is currently the
most common etiological factor in CST.
2) Is there an increased risk for inhaling harmful substances after nasal hair removal?
In a small study involving 75 patients with asthma, the amount of nasal hair was inversely correlated with asthma:
Does nasal hair (vibrissae) density affect the risk of developing asthma in patients with seasonal rhinitis? (International Archieves of Allergy and Immunology, 2011):
The rate of asthma was 44.7, 26.2 and 16.7% in the few, moderate and
many [hair] groups, respectively (p = 0.002).
Our findings suggest that the amount of nasal hair providing a nose
filtration function has a protective effect on the risk of developing
asthma in SR patients.