Csdrhrt

Can women give diksha to either man or woman as per Hindu scriptures?
If no, what is the reason?
If yes, why don't we see woman gurus who give mantras to others much?

Do dharma shastras allow women to be diksha guru?

It's only in the Tantras, that the concept that a woman can be a Guru is allowed. In scriptures like Smritis (Manu Smriti etc) women are not even allowed initiation. So, the question of women becoming Gurus of others is invalid.

From the Tantras, I have been able to find out two such references.

First one:

EkAkshare tathA kute traipure mantra nAyike |
Stri datte swapana
lavdhe cha siddhAdi naiva sAdhayet ||

Oh Goddess of Mantras, in case of one-lettered Mantras (like Om),
Kuta Mantras, Traipura Mantras, Mantras given by a female Guru, or for ones
that are obtained in dreams, SidhAdi considerations are not required to be followed.

KulArnava Tantram 15.98

This verse not only allows a woman giving Mantra DikshA but also says that when they are the Gurus, Sidha-Asiddha and other similar considerations are not required to be followed. So, this makes initiations from female Gurus advantageous because in usual circumstances those things are to be taken into account.

The next set of verses is some TattvasAra Tantram verses quoted in ShAkta Ananda Tarangini's 2nd Chapter:

Striyo dikshA shubhA proktA matush cha astagunA smritA |
Swapno
lavdhA cha yA dikshA tatra nAsti vichAranA ||

Getting intiated from a female Guru is reagrded as auspicious. And,
initiation from the mother is regarded as 8 times more auspicious than
that. When DikshA Mantra is obtained in dreams, no considerations are
required to be followed.

SAdvi chaiva sadAchArA guru bhaktA jitendriyA |
Sarva tantrArtha
sAragyA sadhavA pujane ratA ||
Guru yogyA bhavet sA hi vidhavAm
parivarjayet ||

The SadavA (a female who's husband is alive) female, who is of good
conduct, who is devoted towards her husbad, who has won over her
senses, who is engaged in worship and other similar acts, who has the
knowledge of the meanings of all Tantras is fit to be a Guru. The
Vidhava (or a widow) should be avoided as a Guru.

There is a debate whether a widow can initiate or not and I think the conclusion is that she can not usually but if she is Siddha or the Mantra itself is Siddha then she can.

Yes, of course.Diksha is a tantrik process. In Guptasadhanatantra page 155), the dhyanamantra of female -Guru is provided. In Matri Tantra(page 7), the hymn to female Guru is provided.

Diksha from own mother has been praised very very highly. So all these prove that female gurus have full capacity to initiate.

(Ref: Sastramulak Bharatiya Shaktisadhana, Upendrakumar Das,RMIC, vol.2, chapter 14)

Yes, we have seen many women Gurus. Bhairavi Jogeswari was a Guru of Sri Ramakrishna.His disciples Sri Sarada Devi and Sri Gauri Maa initiated many people. Durgapuri Devi was a disciple of Sarada Devi. She had initiated many and Her successors continue Her lineage from Saradeswari Ashram, Kolkata, so far sas I know.Maa Anandamoyee initiated many people.Maamoni, the wife Of Sri Asimananda Saraswati of Sri Bijaykrishna Goswami lineage was guru of many. Even now Mata Amritanandamoyee is famous as Guru. There are many more in the line.