Incorrect. Red hair is not solely Celtic. Thor's beard was red. Odin's moustache was red. Red hair is common among Germanic people(specifically Nords), but the dark orange looking hair that people associate with gingers is a Celtic trait. The lighter/blonder variation of red hair is a Nordic/Germanic trait. The pic related shows the occurrence of red hair. As you can see, it is very much present on the shores of Northern Germany, Denmark, and Norway. All Germanic.
eupedia.com/genetics/britain_ireland_dna.shtml
If you look at the chart in the link above, you'll see that the I1 y-DNA haplogroup(Nordic) is strongest in Southern and Eastern Scotland(The Lowlands) and is weakest in the West(The Highlands). In fact, it is a higher percentage in Southern Scotland than it is in every other part of Albion besides East Anglia.
Scots, the language, is very close to English compared to other languages, yes, but only because the population of Northumbria, the seed of modern Scotland, was a nation comprised of AngloSaxons(English). Combine that with intermixing with the Scandinavians and you've got yourself a Germanic population. There has been some intermixing between Highlanders and Lowlanders over the ages, but not enough to declassify them as a Germanic people.
The blue map is a collection of multiple y-DNA haplogroups that coincide with Germanic ancestry. As you can see, Scotland is very much Germanic. More so than Eastern Austria and much of Germany's former territories. Keep in mind, when I say Scotland is more Germanic, I say so because the vast majority of Scots are Lowlanders and the vast majority of those Lowlanders live around Edinburgh, which is well within the "50-60%" shade of blue on the map.
Highlanders are very much Celtic. That is undisputable. Highlanders don't even like Lowlanders in Scotland. But the Lowlanders are in fact Germanic. More specifically, they are AngloSaxon, just like the English.
As for their language, Scots is a strange mix of dialect and different language, mainly because they've picked up so much more Norse than the Southerners did. You can see this clearly in "Kinrick". Kinrick means Kingdom in Scots. What do Germans call an kingdom? Königreich. What do Swedes call a kingdom? A rike. What do Danes call a Kingdom? A Kongerige.
The Scots language is English+Scandinavian+lazy ass pronunciation, but make no mistake, it is indeed a language.
sco.wikipedia.org/wiki/Scots_leid