Why did British Gen. Frank Messervy oppose the invasion of Kashmir?

I don't think Messervy did any such thing. There is only one source given for the claim on Wikipedia, that too Hodson, a British official. So take it with a pinch of salt.

But there are at least two good reasons why Messervy should have opposed it:

1. The Pashtun tribes would be unruly and bring disaster.
2. An invasion of Kashmir would force the Maharaja to accede to India, and would be self-defeating for Pakistan.

Both of these actually happened, and they were even predicted ahead of time by even Pakistani officials. That is why Cunningham, the Governor of NWFP, raised a concern.

But Messervy was a macho general. Such wisdom would hardly appeal to him. Rather than opposing, there is in fact evidence that he may have been a chief instigator of the whole thing. See the section called Operation Gulmarg Plan and the footnote [b] given there. The fact that he was relieved of his post in under six months implies that there was something wrong, and damage control has been done.

In October 1947, the armed forces of India and Pakistan remained largely under the command of British officers. General Messervy served as Commander-in-Chief of the Pakistan Army, but was answerable to Field Marshal Auchinleck, the Supreme Commander of the Indian and Pakistan armies.

The details of the division of the Armed Forces of India between India and Pakistan, the command structure that was in place in the years following Partition, and how it came to be, are described in Henry Hodson's The great divide: Britain, India, Pakistan, pp 255 - 265 (available to borrow on Internet Archive).

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General Messervy was undoubtedly aware that British policy at that time was to attempt to de-escalate tensions between the two countries in the wake of the violence that had accompanied Partition. He therefore, presumably, knew what Auchinleck's response was likely to be in the event that Pakistan ordered its army to invade Kashmir (see below), and advised Prime Minister Liaquat Ali Khan accordingly

Your second question appears to show a misunderstanding of General Messervy's role. He was Commander-in-Chief of the Pakistan Army, and so would have had no role in commanding the Pashtun tribesmen who invaded Kashmir. In Messervy's absence, the acting Commander-in-Chief of the Pakistan Army was General Sir Douglas David Gracey. He also had no role in commanding Pashtun tribesmen who invaded Kashmir.

The Pakistan Army officers who did lead the Pashtun tribesmen are discussed below.

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In 1999, Major (Retd) Agha Humayun Amin published a memoir titled THE 1947-48 Kashmir War The war of lost opportunities. The answers to both your questions can be found in that memoir.

For your first question, Amin describes Auchinleck's response when Jinnah ordered General Gracey to attack Kashmir:

It may be noted that Mr Jinnah had ordered General Gracey the British Acting C-in-C (Messervy being on leave) of the Pakistan Army to attack Kashmir. Gracey who had been handpicked by Mr Jinnah on the grounds that Field Marshal Auchinleck the Supreme Commander of both the armies did not allow it! Auchinleck flew to Lahore the next day and convinced Mr Jinnah to retract his order. Auchinleck’s threat that all British officers would be withdrawn in case such an order was pressed further convinced Mr Jinnah into retracting this order.

• p15

General Messervy would, no doubt, have anticipated that response, and would therefore have counselled against ordering the invasion. As we know, that advice was ignored.

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As for the commanders of the Pashtun tribesmen, Khan says the following:

Shaukat [Sardar Shaukat Hayat] was appointed as overall in charge with Major Khurshid Anwar (Retired) commanding the northern tribal force which was as per Akbar’s appreciation to attack on Muzaffarabad-Srinagar axis and Major Zaman Kiani of the INA to command the southern force tasked to operate against the Kathua area in the south.

• p5

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Major Amin's book is also available on Internet Archive. If you are interested in further detail, you may find the links to sources provided in the chapter endnotes of use.