I read somewhere that the flood of Noah did not affect Israel. If so, why were there no survivors there?
also, where did the olive branch come from if all trees were destroyed. From Israel?
It is a dispute in Bereishis Rabbah 33:6 whether Eretz Yisrael was flooded. According to R’ Beivai, who holds that it was flooded, the inhabitants obviously died. According to R’ Abba bar Kahana and R’ Levi, who hold that it was not flooded, there was still a massive amount of water coming in from neighboring lands; what the Midrash means is that it wasn’t flooded directly (see Ramban and Rabbeinu Bachaye to Bereishis 8:11, and Alshich to Bereishis 8:9).
On to your second question. The Midrash Ibid. addresses this as well. According to R’ Abba and R’ Levi, the trees were still strong enough to avoid being knocked over. Thus, the dove got the olive branch from Mount of Olives. According to R’ Beivai, the dove flew to Gan Eden and got an olive branch from there.
The Midrash at hand:
מֵהֵיכָן הֵבִיאָה אוֹתוֹ, רַבִּי אַבָּא בַּר כַּהֲנָא אָמַר מִשַּׁבְשׁוּשִׁין שֶׁבְּאֶרֶץ יִשְׂרָאֵל הֵבִיאָה אוֹתוֹ. רַבִּי לֵוִי אָמַר מֵהַר הַמִּשְׁחָה הֵבִיאָה אוֹתוֹ, דְּלָא טְפָת אַרְעָא דְּיִשְׂרָאֵל בְּמַבּוּלָא, וְהוּא שֶׁהַקָּדוֹשׁ בָּרוּךְ הוּא אוֹמֵר לִיחֶזְקֵאל (יחזקאל כב, כד): אֶרֶץ לֹא מְטֹהָרָה הִיא לֹא גֻשְׁמָהּ בְּיוֹם זָעַם. רַב בֵּיבַי אָמַר נִפְתְּחוּ לָהּ שַׁעֲרֵי גַן עֵדֶן וְהֵבִיאָה אוֹתוֹ.
TL;DR It is a matter of dispute in Zevahim whether or not Israel was inundated by the flood. According to the opinion that it was not, there is some indication that some animals and / or people survived there. Other commentators, however, and the passage in Zevahim indicate that according to both opinions everyone there died. Regarding the olive leaf, the simple assumption is that the trees simply stood. The Midrash suggests that the leaf may have been from Israel or according to another opinion, from the Garden of Eden. Other commentators suggest that the trees were destroyed everywhere and the leaf was from a newly grown tree.
It is a matter of dispute in Zevahim (113a) whether the deluge affected Israel [i]. However Pirkei D'rabbi Eliezer (ed. Higger ch. 23) [ii] implies that it was inundated, just not directly rained on. This is also clearly stated by Rabbenu Hayyim Paltiel in his commentary to Genesis (8:11) [iii]. This is also indicated by and by Midrash Maor HaAfelah (Parashat Noah p. 70) and Midrash HaBeiur (Parashat Noah page 58) who both indicate that they are quoting Hazal that while Israel wasn't rained on, that it was inundated with water from elsewhere. Indeed, in Zevahim there (113b) [iv], both R. Yohanan who holds it didn't affect Israel, and Resh Lakish who holds it did, seem to agree that everyone other than Noah and his family died.
However, the Hizkuni (Genesis 6:14) [v] indicates that according to the opinion that Israel was not inundated that people survived there.
Indeed, Rashi to Nidda (61a) writes that in chapter Helek in Sanhedrin, it is stated that Og survived by fleeing to Israel. Evidently, at least according to the opinion that Israel wasn't subject to the flood, there were survivors there.[vi]
Similarly, in discussing the survival of the re'em; some sort of large creature, the Talmud (Zevahim there) suggests that it survived in Israel. Accordingly, apparently at least animals in Israel could have survived. Perhaps according to this suggestion, people could have survived as well.
As noted by Ramban (Genesis 8:11), the simple answer regarding the dove was that the trees were not destroyed. The point of sending it was to see if it was safe to exit the ark. Had the dove flown off to Israel, that would have said nothing about whether it was safe to exit.
However, the Midrash Lekah Tov (Genesis 8:11) cites two views either that it was from Israel, or that it was from the Garden of Eden:
ומאין הביאה היונה את העלה הזה, ר' לוי אמר מארץ ישראל הביאה שלא נשטפה במבול, שכן הוא אומר ביחזקאל (יחזקאל כב כד) בן אדם אמור לה את ארץ לא מטהורה היא, לא גושמה ביום זעם... ר' קיראי אמר נפתחו לה שערי גן עדן והביאה העלה, ולמה זית, אמרה לו מוטב לי מר מזה, ולא מתוק מידך לפי שנלאו בתבה:
Interestingly, Abravanel (Parashat Noah ch. 8) holds that neither answer is sufficient. The latter, since it is derash and not peshat, and the former, since he assumes that not only would the floodwaters have felled the trees, but even the indirect inundation that Israel received would have felled the trees! Therefore, he suggests that broken olive branches floated on top of the water, and when the water receded sufficiently some of them took root, and the dove retrieved a leaf of one of these new olive trees.
[i] Zevahim 113a:
מר סבר: ירד מבול לא"י, ומר סבר: לא ירד
One held the deluge descended upon Israel, one held it did not descend on Israel.
[ii] Pirkei D'rabbi Eliezer (ed. Higger ch. 23):
חוץ מארץ ישראל שלא ירדה עליה מבול מן השמים, אלא נתגלגלו המים מכל הארצות
[iii] Rabbenu Hayyim Paltiel's commentary to Genesis (8:11) [iii]:
אעפ"י שלא ירד שם מבול מ"מ נתגלגלו ושט(ט)פו שם המים
[iv] Zevahim (113b):
איתיביה: מכל אשר בחרבה מתו; בשלמא לדידי דאמינא ירד מבול לא"י, משום הכי מתו, אלא לדידך אמאי מתו? משום הבלא
That is, even according to R. Yohanan, in Israel they were killed with "hevel" (apparently this means heat or hot steam). It should be noted that it seems that the Talmud and the Pirkei D'Rabbi Eliezer disagree about what killed them in Israel if it wasn't the rain.
[v] In discussing the idea that Sihon and Og survived the flood, the Hizkuni states that the water around the ark must not have been so hot, to explain how they survived, according to the opinion that Israel was inundated. The implication, is that according to the opinion that Israel was not inundated, that people there survived.